We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
The Laplace Method for Energy Eigenvalue Problems in Quantum Mechanics.
- Authors
Canfield, Jeremy; Galler, Anna; Freericks, James K.
- Abstract
Quantum mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schrödinger equation for them is solved by using a generalized series solution for the bound states (using the Fröbenius method) and then an analytic continuation for the continuum states (if present). In this work, we present an alternative way to solve these problems, based on the Laplace method. This technique uses a similar procedure for the bound states and for the continuum states. It was originally used by Schrödinger when he solved the wave functions of hydrogen. Dirac advocated using this method too. We discuss why it is a powerful approach to solve all problems whose wave functions are represented in terms of confluent hypergeometric functions, especially for the continuum solutions, which can be determined by an easy-to-program contour integral.
- Subjects
QUANTUM mechanics; NONRELATIVISTIC quantum mechanics; SCHRODINGER equation; HYPERGEOMETRIC functions; PROBLEM solving; EIGENVALUES
- Publication
Quantum Reports, 2023, Vol 5, Issue 2, p370
- ISSN
2624-960X
- Publication type
Article
- DOI
10.3390/quantum5020024