86 research outputs found
A new exactly integrable hypergeometric potential for the Schr\"odinger equation
We introduce a new exactly integrable potential for the Schr\"odinger
equation for which the solution of the problem may be expressed in terms of the
Gauss hypergeometric functions. This is a potential step with variable height
and steepness. We present the general solution of the problem, discuss the
transmission of a quantum particle above the barrier, and derive explicit
expressions for the reflection and transmission coefficients
WKB-approach for the 1D hydrogen atom
Taking into account results of WKB-approximation, we derive exact quantum
energies and wave functions of even and odd states in the one-dimensional
Coulomb potentia
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