Some quantum mechanical solutions in nonrelativistic anti-Snyder framework

In this paper, we investigate nonrelativistic anti-Snyder model in momentum representation and obtain quantum mechanical eigenvalues and eigenfunctions. Using this framework, first, in one dimension, we study a particle in a box and the harmonic oscillator problems. Then, for more investigations, in three dimensions, the quantum mechanical eigenvalues and eigenfunctions of a free particle problem and the radius of the neutron star are obtained.

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On the quantum mechanical solutions with minimal length uncertainty

International Journal of Modern Physics A ◽

10.1142/s0217751x16501013 ◽

2016 ◽

Vol 31 (18) ◽

pp. 1650101 ◽

Cited By ~ 13

Author(s):

Homa Shababi ◽

Pouria Pedram ◽

Won Sang Chung

Keyword(s):

Heat Capacity ◽

Partition Function ◽

Harmonic Oscillator ◽

Internal Energy ◽

Free Particle ◽

Minimal Length ◽

Quantum Mechanical ◽

Uncertainty Principles ◽

Trigonometric Functions ◽

Eigenvalues And Eigenfunctions

In this paper, we study two generalized uncertainty principles (GUPs) including [Formula: see text] and [Formula: see text] which imply minimal measurable lengths. Using two momentum representations, for the former GUP, we find eigenvalues and eigenfunctions of the free particle and the harmonic oscillator in terms of generalized trigonometric functions. Also, for the latter GUP, we obtain quantum mechanical solutions of a particle in a box and harmonic oscillator. Finally we investigate the statistical properties of the harmonic oscillator including partition function, internal energy, and heat capacity in the context of the first GUP.

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EXACT QUANTIZATION RULE AND ITS APPLICATIONS TO PHYSICAL POTENTIALS

International Journal of Modern Physics E ◽

10.1142/s0218301307005661 ◽

2007 ◽

Vol 16 (01) ◽

pp. 189-198 ◽

Cited By ~ 53

Author(s):

SHI-HAI DONG ◽

D. MORALES ◽

J. GARCÍA-RAVELO

Keyword(s):

Harmonic Oscillator ◽

Analytical Solutions ◽

Bound States ◽

Energy Levels ◽

Present Approach ◽

Three Dimensions ◽

One Dimension ◽

Quantization Rule ◽

Exact Quantization Rule ◽

Pseudoharmonic Oscillator

By using the exact quantization rule, we present analytical solutions of the Schrödinger equation for the deformed harmonic oscillator in one dimension, the Kratzer potential and pseudoharmonic oscillator in three dimensions. The energy levels of all the bound states are easily calculated from this quantization rule. The normalized wavefunctions are also obtained. It is found that the present approach can simplify the calculations.

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