A recursion relation for matrix elements of the quantum bouncer. Comment on “A quantum bouncing ball,” by Julio Gea-Banacloche [Am. J. Phys. 67 (9), 776–782 (1999)]

2000/09/01 by David M. Goodmanson · 2 citations
Physics and Astronomy · #Quantum Mechanics and Applications #Mechanical and Optical Resonators #Atomic and Subatomic Physics Research

paper · doi:10.1119/1.1302731

Abstract

This paper describes a recursion relation for matrix elements of the quantum bouncer. The relation provides an exact expression for the normalization integral, and allows recursive calculation of matrix elements of the form 〈n|zp|m〉, where z is the spatial coordinate and |m〉,|n〉 are quantum bouncer eigenstates.

Cited by

• Generalized Boundary Conditions for the qBounce Experiment
• Gravitational searches for Lorentz violation with ultracold neutrons

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