Hyers–Ulam stability of the time independent Schrödinger equations

The Approximation Property of a One-Dimensional, Time Independent Schrödinger Equation with a Hyperbolic Potential Well

“…Indeed, Obłoza dealt with Hyers-Ulam stability of the linear differential equation y (x) + f (x)y(x) = g(x). Since then, many mathematicians have become interested in this subject and they have dealt with it more broadly and in depth (see [3,[10][11][12][13][14][15][16][17][18][19][20]).…”

“…Finally, we need to mention that we wrote this paper using the ideas and experience of the papers [16,18,21,22].…”

Perturbation of the one-dimensional time-independent Schrödinger equation with a rectangular potential barrier

“…was investigated when the relevant system has a potential well of finite depth. The ideas of papers [8,9] have a great influence on the present paper. The Schrödinger equation based on postulates of quantum mechanics is a time-dependent equation which yields a time-independent equation that is useful for calculating energy eigenvalues.…”

“…was studied in [8], where α and β are complex numbers (see also [14,15]). In a later paper [9], the Hyers-Ulam stability of the one-dimensional time-independent Schrödinger equation…”

“…In fact, Obloza demonstrated the Hyers-Ulam stability of the linear differential equation ′( ) + ( ) ( ) = ( ) y x g x y x r x . Thereafter, a number of mathematicians have dealt with this subject (see [6][7][8][9][10][11][12][13]).…”