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
Exactly Solvable Schrödinger Operators
✍ Scribed by Jan Dereziński; Michał Wrochna
- Publisher
- Springer
- Year
- 2011
- Tongue
- English
- Weight
- 287 KB
- Volume
- 12
- Category
- Article
- ISSN
- 1424-0637
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract Exactly solvable Schrödinger equation (SE) with a position‐dependent mass distribution allowing Morse‐like eigenvalues is presented. For this, the position‐dependent mass Schrödinger equation is transformed into a standard SE, with constant mass, by means of the point canonical transfor
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 ce
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
## Abstract The solution to a spectral problem involving the Schrödinger equation for a particular class of multiparameter exponential‐type potentials is presented. The proposal is based on the canonical transformation method applied to a general second‐order differential equation, multiplied by a