How Did Schrödinger Get His Equation?

Doug Jensen

Ursula Carow-Watamura, Satoshi Watamura

We consider the q-deformed Schrödinger equation of the harmonic oscillator on the N-dimensional quantum Euclidean space. The creation and annihilation operators are found, which systematically produce all energy levels and eigenfunctions of the Schrödinger equation. In order to get the q series representation of the eigenfunction, we also give an alternative way to solve the Schrödinger equation which is based on the q analysis. We represent the Schrödinger equation by the q difference equation and solve it by using q polynomials and q exponential functions.

Shan Gao

C. Tezcan, R. Sever

Effective mass Schrödinger equation is solved exactly for a given potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function. The effective mass Schrödinger equation is also solved for the Morse potential transforming to the constant mass Schrödinger equation for a potential. One can also get solution of the effective mass Schrödinger equation starting from the constant mass Schrödinger equation. PACS numbers: 03.65.-w; 03.65.Ge; 12.39.Fd Keywords: Position-dependent mass, Effective mass Schrödinger equation, Morse potential, Nikiforov-Uvarov method

Thomas B. Andrews

Hirokazu Tezuka

It is shown that the Schrodinger equation with a linear confinement potential has an analytical solution. The existence of the analytical solution requires additional terms to the potential other than the linear one. The Coulomb-type potential is necessary to get non-zero energy eigenvalues. The author proposes an asymptotically linear potential, and shows that one can analytically solve the Schrodinger equation with this potential.