Solved Problems in Quantum Mechanics and its Applications

Rohit Gupta, Tarun Singhal, Dr. Dinesh Verma

In this paper, we illustrate an application of the Laplace transformation for finding the quantum mechanical Reflection and Transmission coefficients for a particle through a one-dimensional vertical step potential. Quantum mechanics is one of the branches of physics in which the physical problems are solved by algebraic and analytic methods. By applying the Laplace transformation, we can find the quantum mechanical Reflection and Transmission coefficients for a particle through a one-dimensional vertical step potential. Generally, the Laplace transformation has been applied in different areas of science and engineering and makes it easier to solve the problems inengineering applications. It is a mathematical tool which has been put to use for solving the differential equations without finding their general solutions. It has applications in nearly all science and engineering disciplines like analysis of electrical circuits, heat and mass transfer, fluid dynamics, nuclear physics, process controls, quantum mechanical problems,etc.

Leonardo Angelini

Raymond J. Seeger

Martin Pomares Calero

Feynman’s diagrams are a good symbolic tool for the calculation of path integrals en elementary particle physics. Therefore, currently in physics there is an interest to apply quantum mechanics to classical mechanics. It implies that is important also contribute to the development of the theory of path integrals applied to problems of classical mechanics which this is one of the first works in that approach. This kind of research works in theoretical physics is a basis to study the application of Feynman’s diagrams as a way of symbolic algebra to solve problems of classical interactions as if it were of the quantum. In that sense, the author has regarded in basic way the application of the computational tool as FeynCalc, supported by Mathematic 8.0. As a consequence, FeynCalc was used to simulate a semi classical problem with an equivalent of a quantum representation. And the only regarded aspect of representing a classical problem into the quantum approach, this research contributes to a symbolic representation of the physics, where some classical problem can be solved regarding quantum mechanism.

Yang Han-song

It's a very important content in quantum mechanics to solve the problems of potential wells or potential hills. The deep acknowledgement and accurate application of the boundary conditions are an important link to the solution of the problems of this kind. But most of the current quantum mechanics textbooks have not provided a complete reasoning to the boundary conditions. They only directly provide the corresponding boundary condition in the solution of a problem or make an explanation in words according to its physics meaning Aiming at the above insufficiency, this article deduces the boundary conditions from the point of mathematics and simply discusses its scope of application.