Bibliographic Details
| 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] |
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| Database: |
Engineering Source |
