Auxiliary fields as a tool for computing analytical solutions of the Schrödinger equation

Details Auxiliary fields as a tool for computing analytical solutions of the Schrödinger equation Auxiliary fields as a tool for computing analytical solutions of the Schrödinger equation

2008-02-25

arxiv.org/abs/0802.3601v2

J. Phys. A: Math. Theor. 41 (2008) 275301

Physics

Quantum Physics

2 figures

Scientific paper

10.1088/1751-8113/41/27/275301

We propose a new method to obtain approximate solutions for the Schr\"{o}dinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows in many cases to find analytical solutions. It offers a convenient way to study the qualitative features of the energy spectrum of bound states in any potential. In particular, we illustrate our method by solving the case of central potentials with power-law form and with logarithmic form. For these types of potentials, we propose very accurate analytical energy formulae which improve a lot the corresponding formulae that can be found in literature.

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