Generalized Extended Momentum Operator

• URL: http://arxiv.org/abs/2002.10219v1
• Date: Mon, 24 Feb 2020 13:19:01 GMT
• Title: Generalized Extended Momentum Operator
• Authors: M. Izadparast and S. Habib Mazharimousavi
• Abstract summary: 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( xright) $, in such a combination that not only GEMO satisfies the EUP relation but also it is Hermitian.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 Schr\"{o}dinger equation. Upon using the so called point canonical transformation (PCT), we transform the generalized Schr\"{o}dinger equation from $x$-space to $z$-space where in terms of the transformed coordinate, $z$, it is of the standard form of the Schr\"{o}dinger equation. In continuation, we study two illustrative examples and solve the corresponding equations analytically to find the energy spectrum.

Related papers

• Operator Growth in Disordered Spin Chains: Indications for the Absence of Many-Body Localization [0.0]
  We derive general bounds for the operator norm of this commutator in free and interacting fermionic systems. We show, in particular, that in a localized system the norm does grow at most exponentially.
  arXiv  Detail & Related papers  (2024-01-16T00:57:09Z)
• The Schmidt rank for the commuting operator framework [58.720142291102135]
  The Schmidt rank is a measure for the entanglement dimension of a pure bipartite state. We generalize the Schmidt rank to the commuting operator framework. We analyze bipartite states and compute the Schmidt rank in several examples.
  arXiv  Detail & Related papers  (2023-07-21T14:37:33Z)
• Quantum Current and Holographic Categorical Symmetry [62.07387569558919]
  A quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension.
  arXiv  Detail & Related papers  (2023-05-22T11:00:25Z)
• New insights on the quantum-classical division in light of Collapse Models [63.942632088208505]
  We argue that the division between quantum and classical behaviors is analogous to the division of thermodynamic phases. A specific relationship between the collapse parameter $(lambda)$ and the collapse length scale ($r_C$) plays the role of the coexistence curve in usual thermodynamic phase diagrams.
  arXiv  Detail & Related papers  (2022-10-19T14:51:21Z)
• Self-Adjointness of Toeplitz Operators on the Segal-Bargmann Space [62.997667081978825]
  We prove a new criterion that guarantees self-adjointness of Toeplitz operator with unbounded operator-valued symbols. We extend the Berger-Coburn estimate to the case of vector-valued Segal-Bargmann spaces.
  arXiv  Detail & Related papers  (2022-02-09T19:14:13Z)
• Holomorphic family of Dirac-Coulomb Hamiltonians in arbitrary dimension [0.0]
  We study massless 1-dimensional Dirac-Coulomb Hamiltonians, that is, operators on the half-line of the form $D_omega,lambda:=beginbmatrix-fraclambda+omegax&-partial_x.
  arXiv  Detail & Related papers  (2021-07-08T11:48:57Z)
• Quantum scrambling of observable algebras [0.0]
  quantum scrambling is defined by how the associated physical degrees of freedom get mixed up with others by the dynamics. This is accomplished by introducing a measure, the geometric algebra anti-correlator (GAAC) of the self-orthogonalization of the commutant of $cal A$ induced by the dynamics. For generic energy spectrum we find explicit expressions for the infinite-time average of the GAAC which encode the relation between $cal A$ and the full system of Hamiltonian eigenstates.
  arXiv  Detail & Related papers  (2021-07-02T14:30:58Z)
• Anharmonic oscillator: a solution [77.34726150561087]
  The dynamics in $x$-space and in $(gx)-space corresponds to the same energy spectrum with effective coupling constant $hbar g2$. A 2-classical generalization leads to a uniform approximation of the wavefunction in $x$-space with unprecedented accuracy.
  arXiv  Detail & Related papers  (2020-11-29T22:13:08Z)
• Sub-bosonic (deformed) ladder operators [62.997667081978825]
  We present a class of deformed creation and annihilation operators that originates from a rigorous notion of fuzziness. This leads to deformed, sub-bosonic commutation relations inducing a simple algebraic structure with modified eigenenergies and Fock states. In addition, we investigate possible consequences of the introduced formalism in quantum field theories, as for instance, deviations from linearity in the dispersion relation for free quasibosons.
  arXiv  Detail & Related papers  (2020-09-10T20:53:58Z)
• $\mathcal{PT}$-Symmetric Generalized Extended Momentum Operator [0.0]
  We develop further the concept of generalized extended momentum operator (GEMO) In analogy with GEMO, the $mathcalPT$-symmetric GEMO satisfies the extended uncertainty principle (EUP) relation. We apply our formalism to a quasi-free quantum particle and the exact solutions for the energy spectrum are presented.
  arXiv  Detail & Related papers  (2020-06-04T13:24:33Z)
• Generalized geometric commutator theory and quantum geometric bracket and its uses [0.0]
  Inspired by the geometric bracket for the generalized covariant Hamilton system, we abstractly define a generalized geometric commutator $$left[ a,b right]=left[ a,b right]_cr+Gleft(s, a,b right)$$ formally equipped with geomutator $Gleft(s, a,b right)=aleft[ s,b right]_cr-bleft[ s,a right]_cr$ defined in terms
  arXiv  Detail & Related papers  (2020-01-23T14:53:12Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.