What is lowest energy?











up vote
1
down vote

favorite












In many textbook i come up with the term of lowest energy. For example in atomic structures electrons are placed in orbitals in order the atom to have the lowest energy? but what is this energy? potential or kinetic or the sum of the two?






quantum-mechanics energy hilbert-space ground-state







share|cite|improve this question




















  • 3




    The sum of the two, usually the eigenvalue of the Hamiltonian operator.
    – Lewis Miller
    5 hours ago















up vote
1
down vote

favorite












In many textbook i come up with the term of lowest energy. For example in atomic structures electrons are placed in orbitals in order the atom to have the lowest energy? but what is this energy? potential or kinetic or the sum of the two?






quantum-mechanics energy hilbert-space ground-state







share|cite|improve this question




















  • 3




    The sum of the two, usually the eigenvalue of the Hamiltonian operator.
    – Lewis Miller
    5 hours ago













up vote
1
down vote

favorite









up vote
1
down vote

favorite











In many textbook i come up with the term of lowest energy. For example in atomic structures electrons are placed in orbitals in order the atom to have the lowest energy? but what is this energy? potential or kinetic or the sum of the two?






quantum-mechanics energy hilbert-space ground-state







share|cite|improve this question















In many textbook i come up with the term of lowest energy. For example in atomic structures electrons are placed in orbitals in order the atom to have the lowest energy? but what is this energy? potential or kinetic or the sum of the two?






quantum-mechanics energy hilbert-space ground-state




quantum-mechanics energy hilbert-space ground-state






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 4 hours ago









Qmechanic♦

100k121821135




100k121821135










asked 5 hours ago









ado sar

1288




1288








  • 3




    The sum of the two, usually the eigenvalue of the Hamiltonian operator.
    – Lewis Miller
    5 hours ago














  • 3




    The sum of the two, usually the eigenvalue of the Hamiltonian operator.
    – Lewis Miller
    5 hours ago








3




3




The sum of the two, usually the eigenvalue of the Hamiltonian operator.
– Lewis Miller
5 hours ago




The sum of the two, usually the eigenvalue of the Hamiltonian operator.
– Lewis Miller
5 hours ago










3 Answers
3






active

oldest

votes

















up vote
2
down vote













The sum of the two.



An electronic state like an orbital is an exact or approximate solution of some time independent Schrödinger equation, i.e. an eigenstate of the hamiltonian made by a kinetic and a potential energy term. The corresponding eigenvalue is the expectation value of such hamiltonian, evaluated on the state described by the orbital.



The expectation value of the hamiltonian can always be written as the sum of the expectation value of kinetic and potential energy. The lowest energy, is the eigenvalue of the hamiltonian with the minimum value.






share|cite|improve this answer




























    up vote
    2
    down vote













    The lowest energy of a quantum system is the minimum eigenvalue of the Hamiltonian of the system. The Hamiltonian is the operator which corresponds to the total energy of the system, so it is the sum of the kinetic and potential energy. This is often also referred to as the ground state energy of the system.




    but what is this energy?




    Heuristically, the ground state energy is the energy which the system has simply by existing. Normally, this doesn't make any sense: If I just make the system do nothing, just sit there, then it would have zero energy. We wouldn't need the fancy name.



    But it turns out that this is impossible. We can never "pin down" a system and make it completely still, due to the famous Heisenberg uncertainty principle,
    $$Delta x Delta p geq hbar/2.$$
    The system must have some momentum, to satisfy the inequality. In turn, it will also have some energy. This is why we can never reach absolute zero! No matter how hard we try, there always remains the jiggling of the ground state.






    share|cite|improve this answer




























      up vote
      1
      down vote













      In QM the Schrödinger Equation gives you the solutions for the wavefunction of a particle with a given potential. Because the energy is quantized you usually find several possible values for the energy that are given by an integer number $ n $ called the Principal Quantum Number. The lowest value of $ E_n $, normally when $ n=0 $ or $ n=1 $, is the Groud-State. This means that the energy of the particle is the lowest and it is a combination of the potential energy and the kinetic energy.






      share|cite|improve this answer





















        Your Answer





        StackExchange.ifUsing("editor", function () {
        return StackExchange.using("mathjaxEditing", function () {
        StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
        StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
        });
        });
        }, "mathjax-editing");

        StackExchange.ready(function() {
        var channelOptions = {
        tags: "".split(" "),
        id: "151"
        };
        initTagRenderer("".split(" "), "".split(" "), channelOptions);

        StackExchange.using("externalEditor", function() {
        // Have to fire editor after snippets, if snippets enabled
        if (StackExchange.settings.snippets.snippetsEnabled) {
        StackExchange.using("snippets", function() {
        createEditor();
        });
        }
        else {
        createEditor();
        }
        });

        function createEditor() {
        StackExchange.prepareEditor({
        heartbeatType: 'answer',
        convertImagesToLinks: false,
        noModals: true,
        showLowRepImageUploadWarning: true,
        reputationToPostImages: null,
        bindNavPrevention: true,
        postfix: "",
        imageUploader: {
        brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
        contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
        allowUrls: true
        },
        noCode: true, onDemand: true,
        discardSelector: ".discard-answer"
        ,immediatelyShowMarkdownHelp:true
        });


        }
        });














        draft saved

        draft discarded


















        StackExchange.ready(
        function () {
        StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f448569%2fwhat-is-lowest-energy%23new-answer', 'question_page');
        }
        );

        Post as a guest















        Required, but never shown

























        3 Answers
        3






        active

        oldest

        votes








        3 Answers
        3






        active

        oldest

        votes









        active

        oldest

        votes






        active

        oldest

        votes








        up vote
        2
        down vote













        The sum of the two.



        An electronic state like an orbital is an exact or approximate solution of some time independent Schrödinger equation, i.e. an eigenstate of the hamiltonian made by a kinetic and a potential energy term. The corresponding eigenvalue is the expectation value of such hamiltonian, evaluated on the state described by the orbital.



        The expectation value of the hamiltonian can always be written as the sum of the expectation value of kinetic and potential energy. The lowest energy, is the eigenvalue of the hamiltonian with the minimum value.






        share|cite|improve this answer

























          up vote
          2
          down vote













          The sum of the two.



          An electronic state like an orbital is an exact or approximate solution of some time independent Schrödinger equation, i.e. an eigenstate of the hamiltonian made by a kinetic and a potential energy term. The corresponding eigenvalue is the expectation value of such hamiltonian, evaluated on the state described by the orbital.



          The expectation value of the hamiltonian can always be written as the sum of the expectation value of kinetic and potential energy. The lowest energy, is the eigenvalue of the hamiltonian with the minimum value.






          share|cite|improve this answer























            up vote
            2
            down vote










            up vote
            2
            down vote









            The sum of the two.



            An electronic state like an orbital is an exact or approximate solution of some time independent Schrödinger equation, i.e. an eigenstate of the hamiltonian made by a kinetic and a potential energy term. The corresponding eigenvalue is the expectation value of such hamiltonian, evaluated on the state described by the orbital.



            The expectation value of the hamiltonian can always be written as the sum of the expectation value of kinetic and potential energy. The lowest energy, is the eigenvalue of the hamiltonian with the minimum value.






            share|cite|improve this answer












            The sum of the two.



            An electronic state like an orbital is an exact or approximate solution of some time independent Schrödinger equation, i.e. an eigenstate of the hamiltonian made by a kinetic and a potential energy term. The corresponding eigenvalue is the expectation value of such hamiltonian, evaluated on the state described by the orbital.



            The expectation value of the hamiltonian can always be written as the sum of the expectation value of kinetic and potential energy. The lowest energy, is the eigenvalue of the hamiltonian with the minimum value.







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered 5 hours ago









            GiorgioP

            1,199212




            1,199212






















                up vote
                2
                down vote













                The lowest energy of a quantum system is the minimum eigenvalue of the Hamiltonian of the system. The Hamiltonian is the operator which corresponds to the total energy of the system, so it is the sum of the kinetic and potential energy. This is often also referred to as the ground state energy of the system.




                but what is this energy?




                Heuristically, the ground state energy is the energy which the system has simply by existing. Normally, this doesn't make any sense: If I just make the system do nothing, just sit there, then it would have zero energy. We wouldn't need the fancy name.



                But it turns out that this is impossible. We can never "pin down" a system and make it completely still, due to the famous Heisenberg uncertainty principle,
                $$Delta x Delta p geq hbar/2.$$
                The system must have some momentum, to satisfy the inequality. In turn, it will also have some energy. This is why we can never reach absolute zero! No matter how hard we try, there always remains the jiggling of the ground state.






                share|cite|improve this answer

























                  up vote
                  2
                  down vote













                  The lowest energy of a quantum system is the minimum eigenvalue of the Hamiltonian of the system. The Hamiltonian is the operator which corresponds to the total energy of the system, so it is the sum of the kinetic and potential energy. This is often also referred to as the ground state energy of the system.




                  but what is this energy?




                  Heuristically, the ground state energy is the energy which the system has simply by existing. Normally, this doesn't make any sense: If I just make the system do nothing, just sit there, then it would have zero energy. We wouldn't need the fancy name.



                  But it turns out that this is impossible. We can never "pin down" a system and make it completely still, due to the famous Heisenberg uncertainty principle,
                  $$Delta x Delta p geq hbar/2.$$
                  The system must have some momentum, to satisfy the inequality. In turn, it will also have some energy. This is why we can never reach absolute zero! No matter how hard we try, there always remains the jiggling of the ground state.






                  share|cite|improve this answer























                    up vote
                    2
                    down vote










                    up vote
                    2
                    down vote









                    The lowest energy of a quantum system is the minimum eigenvalue of the Hamiltonian of the system. The Hamiltonian is the operator which corresponds to the total energy of the system, so it is the sum of the kinetic and potential energy. This is often also referred to as the ground state energy of the system.




                    but what is this energy?




                    Heuristically, the ground state energy is the energy which the system has simply by existing. Normally, this doesn't make any sense: If I just make the system do nothing, just sit there, then it would have zero energy. We wouldn't need the fancy name.



                    But it turns out that this is impossible. We can never "pin down" a system and make it completely still, due to the famous Heisenberg uncertainty principle,
                    $$Delta x Delta p geq hbar/2.$$
                    The system must have some momentum, to satisfy the inequality. In turn, it will also have some energy. This is why we can never reach absolute zero! No matter how hard we try, there always remains the jiggling of the ground state.






                    share|cite|improve this answer












                    The lowest energy of a quantum system is the minimum eigenvalue of the Hamiltonian of the system. The Hamiltonian is the operator which corresponds to the total energy of the system, so it is the sum of the kinetic and potential energy. This is often also referred to as the ground state energy of the system.




                    but what is this energy?




                    Heuristically, the ground state energy is the energy which the system has simply by existing. Normally, this doesn't make any sense: If I just make the system do nothing, just sit there, then it would have zero energy. We wouldn't need the fancy name.



                    But it turns out that this is impossible. We can never "pin down" a system and make it completely still, due to the famous Heisenberg uncertainty principle,
                    $$Delta x Delta p geq hbar/2.$$
                    The system must have some momentum, to satisfy the inequality. In turn, it will also have some energy. This is why we can never reach absolute zero! No matter how hard we try, there always remains the jiggling of the ground state.







                    share|cite|improve this answer












                    share|cite|improve this answer



                    share|cite|improve this answer










                    answered 4 hours ago









                    Hanting Zhang

                    37216




                    37216






















                        up vote
                        1
                        down vote













                        In QM the Schrödinger Equation gives you the solutions for the wavefunction of a particle with a given potential. Because the energy is quantized you usually find several possible values for the energy that are given by an integer number $ n $ called the Principal Quantum Number. The lowest value of $ E_n $, normally when $ n=0 $ or $ n=1 $, is the Groud-State. This means that the energy of the particle is the lowest and it is a combination of the potential energy and the kinetic energy.






                        share|cite|improve this answer

























                          up vote
                          1
                          down vote













                          In QM the Schrödinger Equation gives you the solutions for the wavefunction of a particle with a given potential. Because the energy is quantized you usually find several possible values for the energy that are given by an integer number $ n $ called the Principal Quantum Number. The lowest value of $ E_n $, normally when $ n=0 $ or $ n=1 $, is the Groud-State. This means that the energy of the particle is the lowest and it is a combination of the potential energy and the kinetic energy.






                          share|cite|improve this answer























                            up vote
                            1
                            down vote










                            up vote
                            1
                            down vote









                            In QM the Schrödinger Equation gives you the solutions for the wavefunction of a particle with a given potential. Because the energy is quantized you usually find several possible values for the energy that are given by an integer number $ n $ called the Principal Quantum Number. The lowest value of $ E_n $, normally when $ n=0 $ or $ n=1 $, is the Groud-State. This means that the energy of the particle is the lowest and it is a combination of the potential energy and the kinetic energy.






                            share|cite|improve this answer












                            In QM the Schrödinger Equation gives you the solutions for the wavefunction of a particle with a given potential. Because the energy is quantized you usually find several possible values for the energy that are given by an integer number $ n $ called the Principal Quantum Number. The lowest value of $ E_n $, normally when $ n=0 $ or $ n=1 $, is the Groud-State. This means that the energy of the particle is the lowest and it is a combination of the potential energy and the kinetic energy.







                            share|cite|improve this answer












                            share|cite|improve this answer



                            share|cite|improve this answer










                            answered 37 mins ago









                            Kirtpole

                            1358




                            1358






























                                draft saved

                                draft discarded




















































                                Thanks for contributing an answer to Physics Stack Exchange!


                                • Please be sure to answer the question. Provide details and share your research!

                                But avoid …



                                • Asking for help, clarification, or responding to other answers.

                                • Making statements based on opinion; back them up with references or personal experience.


                                Use MathJax to format equations. MathJax reference.


                                To learn more, see our tips on writing great answers.





                                Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


                                Please pay close attention to the following guidance:


                                • Please be sure to answer the question. Provide details and share your research!

                                But avoid …



                                • Asking for help, clarification, or responding to other answers.

                                • Making statements based on opinion; back them up with references or personal experience.


                                To learn more, see our tips on writing great answers.




                                draft saved


                                draft discarded














                                StackExchange.ready(
                                function () {
                                StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f448569%2fwhat-is-lowest-energy%23new-answer', 'question_page');
                                }
                                );

                                Post as a guest















                                Required, but never shown





















































                                Required, but never shown














                                Required, but never shown












                                Required, but never shown







                                Required, but never shown

































                                Required, but never shown














                                Required, but never shown












                                Required, but never shown







                                Required, but never shown







                                -

                                Popular posts from this blog

                                A CLEAN and SIMPLE way to add appendices to Table of Contents and bookmarks

                                Image
                                0 I found a lot of questions abount appendices and ToC. Many users want appendices to be grouped in an Appendix part, however some problems arise with ToC, hyperref, PDF viewer bookmarks, and so on. There are different solutions which require extra packages, command patching and other extra code, however none of them satisfies me. I almost found an easy way to accomplish a good result, where appendices are added to bookmarks in the right way and hyperref links point to the right page. However, the number of the "Appendix" part page is wrong (it's the number of appendix A). Is there any EASY way to fix that? This is a MWE: documentclass{book} usepackage[nottoc,notlot,notlof]{tocbibind} usepackage{hyperref} begin{document} frontmatter tableofcontents mainmatter part{First} chapter{
                                Read more

                                Calculate evaluation metrics using cross_val_predict sklearn

                                Image
                                1 In the sklearn.model_selection.cross_val_predict page it is stated: Generate cross-validated estimates for each input data point. It is not appropriate to pass these predictions into an evaluation metric. Can someone explain what does it mean? If this gives estimate of Y (y prediction) for every Y (true Y), why can't I calculate metrics such as RMSE or coefficient of determination using these results? python scikit-learn cross-validation share | improve this question edited Nov 28 '18 at 17:52 desertnaut 20.3k 7 43 79
                                Read more

                                Insert data from modal to MySQL (multiple modal on website)

                                Image
                                0 I have problem with inserting data to MySQL from modal. My modal: <a href="#" class="badge badge-pill badge-success">6 komentarzy</a> <a href="#" class="badge badge-pill badge-danger">brak komentarzy</a> <a data-toggle="modal" href="#add_desk_comm_{$desk_['desk_id']}" data-target="#add_desk_comm_{$desk_['desk_id']}" class="ediiit">(dodaj)</a> <div class="modal fade" id="add_desk_comm_{$desk_['desk_id']}" tabindex="-1" role="dialog" aria-labelledby="edit_printer" aria-hidden="true"> <div class="modal-dialog" role="document">
                                Read more