Three-Dimensional Quantum Mechanics: Bound States

S. Brandt, Hans Dieter Dahmen

S. Brandt, Hans Dieter Dahmen

Charles E. Burkhardt, Jacob J. Leventhal

Guillermo Palma, Ulrich Raff

A method is developed to find the bound state eigenvalues and eigenfunctions of one-dimensional and rotational symmetric three-dimensional quantum mechanical problems. The method is based on the fact that eigenfunctions of bound states are square integrable. We use this property and a judicious ansatz inspired on its asymptotic behavior to obtain a differential equation that can be solved straightforwardly using a Fourier transform. The main advantage of the method is that it avoids the traditional and tedious convergence analysis using a series representation. The method leads to an integral representation of the wave function and provides insight into concepts such as energy quantization, spectrum degeneracy, and bound states.

Luis Grave de Peralta, Maricela Fernández Lozada, Hira Farooq +3 more

A Srinivas, Puneet Agarwal

The mathematical formulas of quantum mechanics are those mathematical formalisms that license a thorough depiction of quantum mechanics. This mathematical formalism utilizes essentially a piece of practical examination, particularly Hilbert space which is a sort of linear space. We have explored S-wave bound states made out of three indistinguishable bosons communicating by means of controlled delta work possibilities in non-relativistic quantum mechanics. For low-vitality frameworks, these short-go possibilities fill in as a guess to the basic physics, prompting a compelling field theory. A strategy for perturbatively growing the three-body bound-state condition in reverse powers of the cutoff is created. This permits us to extricate some expository outcomes concerning the behavior of the framework.