Minimal Length and the Quantum Bouncer: A Nonperturbative Study

Abstract

We present the energy eigenvalues of a quantum bouncer in the framework of the Generalized (Gravitational) Uncertainty Principle (GUP) via quantum mechanical and semiclassical schemes. In this paper, we use two equivalent nonperturbative representations of a deformed commutation relation in the form [X,P]=i\hbar(1+\beta P^2) where \beta is the GUP parameter. The new representation is formally self-adjoint and preserves the ordinary nature of the position operator. We show that both representations result in the same modified semiclassical energy spectrum and agrees well with the quantum mechanical description.Comment: 14 pages, 2 figures, to appear in Int. J. Theor. Phy

Massive fermions interacting via a harmonic oscillator in the presence of a minimal length uncertainty relation

“…The Heisenberg algebra we need to study, can be obtained when the commutation relation between the position and momentum is modified from the canonical one to [16]…”

Exact ultra cold neutrons’ energy spectrum in gravitational quantum mechanics

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