Quantum charges of harmonic oscillators

• URL: http://arxiv.org/abs/2404.01756v2
• Date: Wed, 10 Apr 2024 12:45:29 GMT
• Title: Quantum charges of harmonic oscillators
• Authors: Alexander D. Popov,
• Abstract summary: We show that the energy eigenfunctions $psi_n$ with $nge 1$ are complex coordinates on orbifolds $mathbbR2/mathbbZ_n$. We also discuss "antioscillators" with opposite quantum charges and the same positive energy.
• Score: 55.2480439325792
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We discuss Riemannian geometry of one-dimensional quantum harmonic oscillator. Its wavefunction is a holomorphic section of the complex line bundle $L_{\sf{v}}$ over the phase space $\mathbb{R}^2$. We show that the energy eigenfunctions $\psi_n$ with $n\ge 1$, corresponding to the energy levels $E_n$, are complex coordinates on orbifolds $\mathbb{R}^2/\mathbb{Z}_n$ embedded into $L_{\sf{v}}$, where $\mathbb{Z}_n$ is the cyclic group of order $n$. In fact, $\psi_n (t,z)$ is a standing wave on $\mathbb{R}^2/\mathbb{Z}_n$, where $z$ is a complex coordinate on the phase space $\mathbb{R}^2\cong\mathbb{C}$. Oscillators are characterized by two quantum charges $(q_l^{}, q_{\sf{v}})=(n,1)$, where $q_l^{}=n$ is the winding number for the group U(1) acting on $\mathbb{R}^2/\mathbb{Z}_n$ and $q_{\sf{v}}^{}=1$ is the winding number for the U(1)-rotations on fibres of the bundle $L_{\sf{v}}\to\mathbb{R}^2$, and $E_n=\hbar\omega(q_l^{}+\frac{1}{2} q_{\sf{v}}).$ We also discuss "antioscillators" with opposite quantum charges and the same positive energy.

Related papers

• Klein-Gordon oscillators and Bergman spaces [55.2480439325792]
  We consider classical and quantum dynamics of relativistic oscillator in Minkowski space $mathbbR3,1$. The general solution of this model is given by functions from the weighted Bergman space of square-integrable holomorphic (for particles) and antiholomorphic functions on the K"ahler-Einstein manifold $Z_6$.
  arXiv  Detail & Related papers  (2024-05-23T09:20:56Z)
• (2+1)D topological phases with RT symmetry: many-body invariant, classification, and higher order edge modes [6.267386954898001]
  We consider many-body systems of interacting fermions with fermionic symmetry groups $G_f mathbbZf times mathbbZ$. We show that (2+1)D invertible fermionic phases with these symmetries have a $mathbbZ times mathbbZ_8$, $mathbbZ_8$, $mathbbZ2 times mathbbZ$, and $mathbbZ2
  arXiv  Detail & Related papers  (2024-03-27T18:00:00Z)
• Vacuum Force and Confinement [65.268245109828]
  We show that confinement of quarks and gluons can be explained by their interaction with the vacuum Abelian gauge field $A_sfvac$.
  arXiv  Detail & Related papers  (2024-02-09T13:42:34Z)
• Quantum connection, charges and virtual particles [65.268245109828]
  A quantum bundle $L_hbar$ is endowed with a connection $A_hbar$ and its sections are standard wave functions $psi$ obeying the Schr"odinger equation. We will lift the bundles $L_Cpm$ and connection $A_hbar$ on them to the relativistic phase space $T*R3,1$ and couple them to the Dirac spinor bundle describing both particles and antiparticles.
  arXiv  Detail & Related papers  (2023-10-10T10:27:09Z)
• The Hurwitz-Hopf Map and Harmonic Wave Functions for Integer and Half-Integer Angular Momentum [0.0]
  Harmonic wave functions for integer and half-integer angular momentum are given in terms of the angles $(theta,phi,psi)$ that define a rotation in $SO(3)$. A new nonrelistic quantum (Schr"odinger-like) equation for the hydrogen atom that takes into account the electron spin is introduced.
  arXiv  Detail & Related papers  (2022-11-19T19:13:07Z)
• Quantized charge polarization as a many-body invariant in (2+1)D crystalline topological states and Hofstadter butterflies [14.084478426185266]
  We show how to define a quantized many-body charge polarization $vecmathscrP$ for (2+1)D topological phases of matter, even in the presence of non-zero Chern number and magnetic field. We derive colored Hofstadter butterflies, corresponding to the quantized value of $vecmathscrP$, which further refine the colored butterflies from the Chern number and discrete shift.
  arXiv  Detail & Related papers  (2022-11-16T19:00:00Z)
• Monogamy of entanglement between cones [68.8204255655161]
  We show that monogamy is not only a feature of quantum theory, but that it characterizes the minimal tensor product of general pairs of convex cones. Our proof makes use of a new characterization of products of simplices up to affine equivalence.
  arXiv  Detail & Related papers  (2022-06-23T16:23:59Z)
• 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)
• Bulk-boundary asymptotic equivalence of two strict deformation quantizations [0.0]
  The existence of a strict deformation quantization of $X_k=S(M_k(mathbbC))$ has been proven by both authors and K. Landsman citeLMV. A similar result is known for the symplectic manifold $S2subsetmathbbR3$.
  arXiv  Detail & Related papers  (2020-05-09T12:03:18Z)

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.