American Journal of Physics

Solution of the Schrödinger Equation for Some Electric Field Problems

Lawrence H. Buch, Harry H. Denman

Published Apr 1, 1974• 24 citations

Abstract

An alternate treatment of the Schrödinger equation for a charged particle in a uniform, constant electric field is given. The time-varying field is then treated. Next, using a Hamiltonian which gives the classical equations of motion for a particle in a viscous medium subject to a uniform constant, or time-varying field, the corresponding Schrödinger equation is solved. This procedure yields the classical electrical conductivity expressions for both dc and ac fields.

DOI: 10.1119/1.1987677

Related papers

The solution of the Schrödinger equation for finite systems, with special reference to the motion of electrons in Coulomb electric fields and uniform magnetic fields

R. Dingle

ABSTRACT A number of methods are formulated for solving the Schrödinger equation for systems of finite extent. The methods are developed in detail for the particular case of an electron moving in a Coulomb field (e.g. hydrogen-like atom), with a boundary consisting of a sphere of given radius. In the second part of the paper these results are transformed into those for an electron moving in a uniform magnetic field, the boundary of the system being cylindrical.

Mathematical Proceedings of the Cambridge Philosophical SocietyJan 1, 195338 citations

Exact Solutions to Schrödinger Equation for a Charged Particle on a Torus in Uniform Electric and Magnetic Fields

Alexandre G. M. Schmidt

Brazilian Journal of PhysicsJun 21, 202010 citations

Evolution of Arbitrary States under Fock—Darwin Hamiltonian and a Time-Dependent Electric Field

Xiao-Fei Xu, Tao Yang, Zhi-Yuan Zhai +1 more

The method of path integral is employed to calculate the time evolution of the eigenstates of a charged particle under the Fock—Darwin (FD) Hamiltonian subjected to a time-dependent electric field in the plane of the system. An exact analytical expression is established for the evolution of the eigenstates. This result then provides a general solution to the time-dependent Schrödinger equation.

Communications in Theoretical PhysicsJan 1, 20120 citations

Numerical analysis of quantum-mechanical non-uniform E×B drift: Non-uniform electric field

Wataru Kosaka, Shun-ichi Oikawa, Poh Kam Chan

We have numerically solved the two-dimensional time-dependent Schrödinger equation for a charged particle in the presence of a non-uniform electric field E = E ≤(1- y / L_E ) e_y as well as a non-uniform magnetic field B = B ≤(1- y / L_B ) e_z. It is shown that such a non-uniformity of the electric field does not affect the time rate of the variance, or uncertainty, changes in position and momentum, while that of the magnetic field does.

International Journal of Applied Electromagnetics and MechanicsAug 1, 20161 citation

Atoms in strong, oscillating electric fields: momentum-space solutions of the time-dependent, three-dimensional Schrödinger equation

Lee A. Collins, A. L. Merts

We have developed a procedure for solving the three-dimensional, time-dependent Schrödinger equation by expanding the total system wave function in a Volkov basis and by propagating the resulting first-order differential equations in time. We discuss applications to several model systems representing an atom in an intense, oscillating electric field.

Journal of the Optical Society of America BApr 1, 199017 citations

Control of a quantum particle in a moving box

Pierre Rouchon

This 1-D Schrodinger equation describes the non relativistic motion of a single charged particle (mass m = 1, = 1) with a potential V in a uniform electric field t → u(t). With v = −u, (1) represents also the dynamics of a particle in a non Galilean frame of absolute position v (see, e.g., [9]). A change of independent variables (t, q) → (t, z) and dependent variable ψ → φ, transform (1) into (2) where the control appears as a shift on the space variable. These classical transformations are as follows (see, e.g., [2]). Instead of considering u as control, take v defined by v = −u as control. Then

Jan 1, 20024 citations