✍ Scribed by Joseph N Ginocchio
No coin nor oath required. For personal study only.
The one-dimensional Schrodinger equation is solved for a new class of potentials with varying depths and shapes. The energy eigenvalues are given in algebraic form as a function of the depth and shape of the potential.
The eigenfunctions and scattering function are also given in closed form. For certain shapes these potentials resemble the mean field of an atomic nucleus.
📜 SIMILAR VOLUMES
The three-dimensional Schriidinger equation with an effective mass is solved for a new class of angular momentum dependent potentials with varying depths and shapes. The energy eigenvalues and resonances are given in algebraic form as a function of the effective mass and depth and shape of the poten
We construct a general algorithm generating the analytic eigenfunctions as well as eigenvalues of one-dimensional stationary Schrödinger Hamiltonians. Both exact and quasi-exact Hamiltonians enter our formalism but we focus on quasi-exact interactions for which no such general approach has been cons