scholarly journals The spaces of quantum states for some harmonic oscillator potentials on the punctured plane C\{ 0 }

2007 ◽  
Author(s):  
Jan Milewski
Keyword(s):  
Harmonic Oscillator ◽  
Quantum States

scholarly journals A CLASS OF QUANTUM STATES WITH CLASSICAL-LIKE EVOLUTION

1994 ◽  
Vol 08 (29) ◽  
pp. 1823-1831 ◽  
Author(s):  
SALVATORE DE MARTINO ◽  
SILVIO DE SIENA ◽  
FABRIZIO ILLUMINATI
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Quantum States ◽  
Time Dependent ◽  
Stationary States ◽  
Oscillator Potential ◽  
Classical Motion ◽  
Stochastic Formulation ◽  
New States

In the framework of the stochastic formulation of quantum mechanics we derive non-stationary states for a class of time-dependent potentials. The wave packets follow a classical motion with constant dispersion. The new states define a possible extension of the harmonic oscillator coherent states. As an explicit application, we study a sestic oscillator potential.

scholarly journals An atomistic interpretation of Planck's 1900 derivation of his radiation law.

2000 ◽  
Vol 53 (2) ◽  
pp. 193 ◽  
Author(s):  
F. E. Irons
Keyword(s):  
Harmonic Oscillator ◽  
Quantum States ◽  
Max Planck ◽  
Simple Harmonic Oscillator ◽  
Cavity Modes ◽  
Oscillator Models

In deriving his radiation law in 1900, Max Planck employed a simple harmonic oscillator to model the exchange of energy between radiation and matter. Traditionally the harmonic oscillator has been viewed as modelling an entity which is itself oscillating, although a suitable oscillating entity has not been forthcoming. (Opinion is divided between a material oscillator, an imaginary oscillator and a need to revise Planck"s derivation to apply to cavity modes of oscillation). We offer a novel, atomistic interpretation of Planck"s derivation wherein the harmonic oscillator models a transition between the internal quantum states of an atom|not a normal electronic atom characterised by possible energies 0 and hv, but an atom populated by subatomic bosons (such as pions) and characterised by multiple occupancy of quantum states and possible energies nhv (n= 0;1;2; :::). We show how Planck"s derivation can be varied to accommodate electronic atoms. A corollary to the atomistic interpretation is that Planck"s derivation can no longer be construed as support for the postulate that material oscillating entities can have only those energies that are multiples of hv.

scholarly journals QUANTUM STATES OF A GENERALIZED TIME-DEPENDENT INVERTED HARMONIC OSCILLATOR

2004 ◽  
Vol 18 (09) ◽  
pp. 1379-1385 ◽  
Author(s):  
I. A. PEDROSA ◽  
I. GUEDES
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Quantum States ◽  
Time Dependent ◽  
Constant Frequency ◽  
Special Case ◽  
Generalized Time

We discuss the extension of the Lewis and Riesenfeld method of solving the time-dependent Schrödinger equation to cases where the invariant has continuous eigenvalues and apply it to the case of a generalized time-dependent inverted harmonic oscillator. As a special case, we consider a generalized inverted oscillator with constant frequency and exponentially increasing mass.

COMPLETE EXACT QUANTUM STATES OF THE GENERALIZED TIME-DEPENDENT HARMONIC OSCILLATOR

2004 ◽  
Vol 18 (24) ◽  
pp. 1267-1274 ◽  
Author(s):  
I. A. PEDROSA
Keyword(s):  
General Solution ◽  
Harmonic Oscillator ◽  
Exact Solutions ◽  
Continuous Spectrum ◽  
Invariant Operator ◽  
Quantum States ◽  
Time Dependent ◽  
Quadratic Invariants ◽  
Generalized Time ◽  
Discrete And Continuous Spectrum

By making use of linear and quadratic invariants and the invariant operator formulation of Lewis and Riesenfeld, the complete exact solutions of the Schrödinger equation for the generalized time-dependent harmonic oscillator are obtained. It is shown that the general solution of the system under consideration contains both the discrete and continuous spectrum. The connection between linear and quadratic invariants and their corresponding eigenstates via time-dependent auxiliary equations is also established.

WAVE FUNCTIONS WITH DISCRETE AND WITH CONTINUOUS SPECTRUM FOR QUANTUM DAMPED HARMONIC OSCILLATOR PERTURBED BY A SINGULARITY

2004 ◽  
Vol 18 (07) ◽  
pp. 1007-1020 ◽  
Author(s):  
JEONG-RYEOL CHOI
Keyword(s):  
Harmonic Oscillator ◽  
Continuous Spectrum ◽  
Unitary Operator ◽  
Invariant Operator ◽  
Confluent Hypergeometric Function ◽  
Quantum States ◽  
Wave Functions ◽  
The Other ◽  
Damped Harmonic Oscillator ◽  
Discrete And Continuous Spectrum

The quantum states with discrete and continuous spectrum for the damped harmonic oscillator perturbed by a singularity have been investigated using invariant operator and unitary operator together. The eigenvalue of the invariant operator for ω0≤β/2 is continuous while for ω0>β/2 is discrete. The wave functions for ω0=β/2 expressed in terms of the Bessel function and for ω0<β/2 in terms of the Kummer confluent hypergeometric function. The convergence of the probability density is more rapid for over-damped harmonic oscillator than that of the other two cases due to the large damping constant.

A COMPARISON BETWEEN WEHRL–LIEB AND VON NEUMANN ENTROPIES FOR TIME-EVOLVING SPIN-1/2 MIXED STATES

1994 ◽  
Vol 08 (16) ◽  
pp. 995-1006 ◽  
Author(s):  
S. S. MIZRAHI ◽  
V. V. DODONOV ◽  
D. OTERO
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Quantum States ◽  
Alternative Formulation ◽  
Spin States ◽  
Continuous Representation ◽  
Commun Math Phys ◽  
Mixed States ◽  
Von Neumann ◽  
Math Phys

Years ago, A. Wehrl (Rev. Mod. Phys.50, 221 (1978)) introduced the concept of classicallike entropy of quantum states when a two-label continuous representation is used; for instance, the harmonic oscillator coherent states. Subsequently, E. H. Lieb (Commun. Math. Phys.62, 35 (1978)) extended that concept of entropy to the Bloch coherent spin states. Here, we consider spin-1/2 systems and calculate both the Wehrl–Lieb and von Neumann entropies, and then we compare the results and discuss the Wehrl–Lieb entropy as an alternative formulation to von Neumann's. As illustration, three examples are worked out: (i) the decoherence of a quantum state in a measurement process, (ii) the conservation of coherence, and (iii) the recoherence phenomena that appear in the solutions of a specific master equation that originates from a nonlinear Schrödinger equation.

scholarly journals Simulating a Quantum Harmonic Oscillator by Introducing it to a Bosonic System

2020 ◽  
Author(s):  
RAJDEEP TAH
Keyword(s):  
Harmonic Oscillator ◽  
Quantum States ◽  
Unitary Operators ◽  
Quantum Harmonic Oscillator ◽  
Bosonic System ◽  
System P ◽  
Pauli Matrix

The goal of this paper is to associate a Quantum Harmonic Oscillator to a Bosonic System, try to simulate it in IBMQ-Experience (at 8192 shots) and further study it. We associated the concept of Pauli Matrix equivalent to Bosonic Particles and used it to calculate the Unitary Operators which helped us to theoretically visualize each Quantum states and further simulate our system.

Outgrowth of quasi pure states in isolated coupled-harmonic-oscillator

2021 ◽  
Vol 35 (05) ◽  
pp. 2150075
Author(s):  
Tianhai Zeng ◽  
Zhaobin Liu ◽  
Kai Li ◽  
Feng Wang ◽  
Bin Shao
Keyword(s):  
Harmonic Oscillator ◽  
Reference Frame ◽  
Interaction Potential ◽  
Mixed State ◽  
Pure State ◽  
Center Of Mass ◽  
Quantum States ◽  
Pure States ◽  
Position Representation ◽  
Coupled Harmonic Oscillator

Isolated coupled-harmonic-oscillator here is the system of two distinguishable particles coupled with a harmonic oscillator interaction potential. Each particle stays in a mixed state due to entanglement. However, in center-of-mass reference frame, we obtain quasi wavefunction of the first particle expressing quasi pure state by replacing the second coordinate in the total wavefunction. We discuss the similar systems with the first particle and the potential being same and the second mass changing from micro to macro one. Measured by fidelity and coherence, the quasi pure state approaches to the pure state of a usual harmonic oscillator with same mass and similar potential. It conversely shows that the latter purely superposed state in position representation and its coherence originate from those of the first particle, which are related with some neglected macro object and the interaction between them. The current results provide a possible clue to new insights into quantum states.

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