Wavefunction of a Quantum Particle

Alto Osada, Rekishu Yamazaki, Atsushi Noguchi

Jiang, Jhe-Yua;Lin, Jyh Shinga

The Particle in a box (PIAB) is the most representative model to be used and illustrated for exactly solving the Schrodinger equation in quantum physics. However, as the degrees of freedom of this PIAB model from one dimensional case to three dimensional case the solutions of its wavefunction will become more difficult to visualize and comprehend. Therefore, in this research work we employed the most popular python programming language with its diverse workable modules and its diverse visualizing modules to easily obtain the visualizing representation, that is, isosurface, of solvable wavefunction of PIAB model in three dimensional case. Furthermore, this isosurface of wavefunction enables us to explore its interesting properties of wavefunction based on their different nx, ny and nz quantum numbers. Consequently, we are able to gain a very deep insight into this complex wavefunction of PIAB model in three dimensional case.

P. Strange

In this paper we discuss a solution of the free particle Schroodinger equation in which the time and space dependence are not separable. The wavefunction is written as a product of exponential terms, Hermite polynomials and a phase. The peaks in the wavefunction decelerate and then accelerate around t = 0. We analyse this behaviour within both a quantum and a semi-classical regime. We show that the acceleration does not represent true acceleration of the particle but can be related to the envelope function of the allowed classical paths. Comparison with other accelerating wavefunctions is also made. The analysis provides considerable insight into the meaning of the quantum wavefunction.

A.B.M Masum Billah Mim

Pranjal Praneel, Ashish Kumar, Manoj K. Harbola

Abstract Finding wavefunctions for even the simplest of interacting particle systems consisting of two particles is extremely difficult. It is therefore highly desirable that an accurate and easily implementable method be available to instructors and students of quantum-mechanics for obtaining wavefunctions for these particles. The usual approach taken to do this is to use parametrized functional form for the wavefunction in conjunction with the variational method to find approximate wavefunction and energy for the ground-state of such systems. In this paper, we employ random numbers to obtain ground-state wavefunctions and energies of two interacting particles in different one-dimensional potentials. The idea behind using random numbers is to search freely for functions that lead to lower and lower energy, converging eventually to its lowest value. The method presented is easily applicable numerically using a simple algorithm, and the wavefunctions obtained are highly accurate. Thus, the method presented makes study of two interacting particles accessible to instructors and students alike in a transparent manner.