Generalized Extended Momentum Operator

Abstract

We study and generalize the momentum operator satisfying the extended uncertainty principle relation (EUP). This generalized extended momentum operator (GEMO) consists of an arbitrary auxiliary function of position operator, $\mu \left(x\right)$, in such a combination that not only GEMO satisfies the EUP relation but also it is Hermitian. Next, we apply the GEMO to construct the generalized one-dimensional Schrödinger equation. Upon using the so called point canonical transformation (PCT), we transform the generalized Schrödinger equation from $x$-space to $z$-space where in terms of the transformed coordinate, $z$, it is of the standard form of the Schrödinger equation. In continuation, we study two illustrative examples and solve the corresponding equations analytically to find the energy spectrum.

arXiv comment7 pages 2 figures

References in corpus (17)

• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• A Generalized Uncertainty Principle in Quantum Gravity
• Nonpointlike Particles in Harmonic Oscillators
• Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry
• Generalized Uncertainty Principle: Approaches and Applications
• Review on Generalized Uncertainty Principle
• Extended uncertainty principle and the geometry of (anti)-de Sitter space
• Influence of Generalized and Extended Uncertainty Principle on Thermodynamics of FRW universe
• Displacement operator for quantum systems with position-dependent mass
• Morse potential derived from first principles
• Quantum particles trapped in a position-dependent mass barrier; a d-dimensional recipe
• Revisiting the displacement operator for quantum systems with position-dependent mass
• Cosmological Horizons, Uncertainty Principle and Maximum Length Quantum Mechanics
• Quantum mechanics in de Sitter space
• Generalised uncertainty relations for angular momentum and spin in quantum geometry
• Primordial Power Spectra of Cosmological Fluctuations with Generalized Uncertainty Principle and Maximum Length Quantum Mechanics
• A solution to the soccer ball problem for generalised uncertainty relations

Cited by in corpus (2)

• Spectral and thermodynamic properties of supersymmetric quantum systems with self-adjoint deformed momentum
• The Extended Uncertainty Principle from a Projector-Valued Measurement Perspective