Exactly Solvable Problems in Quantum Mechanics

Luca Salasnich

Vladislav G. Bagrov, Dmitriy M. Gitman

Lourdhu Bruno Chandrasekar, Kanagasabapathi Gnanasekar, Marimuthu Karunakaran

Some of the problems in quantum mechanics can be exactly solved without any approximation. Some of the exactly solvable problems are discussed in this chapter. Broadly there are two main approaches to solve such problems. They are (i) based on the solution of the Schrödinger equation and (ii) based on operators. The normalized eigen function, eigen values, and the physical significance of some of the selected problems are discussed.

Grigori Karlovich Giorgadze

In this paper, we investigate the problem of simulation of quantum-mechanical dynamical system with prescribed properties using of exactly solvable Hamiltonians. A method for solving time-dependent matrix Schrodinger equations in an explicit analytical form will be developed. It is based on exactly solvable time-independent problems, a certain choice of the initial conditions, and special time-dependent gauge transformations converting time-independent problems to time-dependent ones. An application of the exactly solvable time-dependent problems thus obtained to the construction of a universal set of gates for quantum computers is also presented.