Formalism of Quantum Mechanics and One Dimensional Problems

Edward L. Hill

Tao Cai

The paper introduces a simplified and exact transfer matrix formalism.That can be used to study a series of one dimensional potential barrier problems with only two general purpose matrices one to propagate a wave function over a region of constant potential,the other to take a wave function over a discontinuity in a potential.Not only are standard results recovered for one potential barrier problem with this technique,but it is easy to extend this formalism into two,even more many potential barier cases,which facilitates wide ranging explorations of one dimensional quantum mechanics.

Douglas Lessie, Joseph Spadaro

The formal theory of multiple scattering in quantum mechanics is adapted to one dimension and applied to the basic problem of scattering by a double delta-function potential. The multiple scattering method is shown to provide a much more powerful analysis than is obtained by either the one-dimensional partial wave approach or by the standard differential solution to the Schrödinger equation.

Richard W. Robinett

Abstract We explore the introduction of Planck’s constant via the study of black body radiation and the need for quantized energies, including the use of statistical mechanics methods to address this problem. This naturally leads to the Sackur Tetrode equation and the connections between entropy and quantum theory. The formalism of quantum mechanics is explored, focusing on the dimensionality of the otherwise formal mathematics involved. Bound states modelling important physical systems (such as the infinite well, harmonic oscillator, linear potential, and the quantum Coulomb problem) are explored in the context of dimensional analysis. The dimensionless phases inherent in quantum wavefunctions are discussed in the context of Planck’s constant, including discussions of some of the classic tests of quantum theory. Systems of units related to aspects of quantum mechanics, including Hartree and Planckian ones, are explored.

Y. B. Band, Y. Avishai