From discrete states to wavefunctions.
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| Title: | From discrete states to wavefunctions. |
|---|---|
| Authors: | Kamela, Martin1 (AUTHOR) mkamela@elon.edu |
| Source: | American Journal of Physics. May2026, Vol. 94 Issue 5, p375-379. 5p. |
| Subjects: | Wave functions, Hilbert space, Quantum mechanics, Quantum operators, Laplacian operator |
| Abstract: | In the spin-first approach to learning quantum mechanics, students explore the 2-state spin Hilbert space before proceeding to wavefunctions and the related infinite-dimensional state space. In this note, we suggest a strategy to help students make this conceptual leap. Approximating continuous space with a finite number of locations, we construct a setting where students' intuition from spin space carries over to a position basis. We derive the position basis representations of the momentum and kinetic energy operators, solve simple bound state problems, and consider limitations to the discrete representation of position. Editor's Note: When teaching the spins-first approach to quantum mechanics, it can be challenging to help students make the transition from working with discrete states of spins to working with continuous states of position and momentum. The author shares an approach in which space is discretized, leading to an approximation of the continuous wavefunction, providing a bridge from discrete to continuous states. [ABSTRACT FROM AUTHOR] |
| Copyright of American Journal of Physics is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 193168970 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: From discrete states to wavefunctions. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kamela%2C+Martin%22">Kamela, Martin</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mkamela@elon.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22American+Journal+of+Physics%22">American Journal of Physics</searchLink>. May2026, Vol. 94 Issue 5, p375-379. 5p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Wave+functions%22">Wave functions</searchLink><br /><searchLink fieldCode="DE" term="%22Hilbert+space%22">Hilbert space</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+mechanics%22">Quantum mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+operators%22">Quantum operators</searchLink><br /><searchLink fieldCode="DE" term="%22Laplacian+operator%22">Laplacian operator</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In the spin-first approach to learning quantum mechanics, students explore the 2-state spin Hilbert space before proceeding to wavefunctions and the related infinite-dimensional state space. In this note, we suggest a strategy to help students make this conceptual leap. Approximating continuous space with a finite number of locations, we construct a setting where students' intuition from spin space carries over to a position basis. We derive the position basis representations of the momentum and kinetic energy operators, solve simple bound state problems, and consider limitations to the discrete representation of position. Editor's Note: When teaching the spins-first approach to quantum mechanics, it can be challenging to help students make the transition from working with discrete states of spins to working with continuous states of position and momentum. The author shares an approach in which space is discretized, leading to an approximation of the continuous wavefunction, providing a bridge from discrete to continuous states. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of American Journal of Physics is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1119/5.0255882 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 5 StartPage: 375 Subjects: – SubjectFull: Wave functions Type: general – SubjectFull: Hilbert space Type: general – SubjectFull: Quantum mechanics Type: general – SubjectFull: Quantum operators Type: general – SubjectFull: Laplacian operator Type: general Titles: – TitleFull: From discrete states to wavefunctions. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kamela, Martin IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00029505 Numbering: – Type: volume Value: 94 – Type: issue Value: 5 Titles: – TitleFull: American Journal of Physics Type: main |
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