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.

QUANTUM STATES WITH CONTINUOUS SPECTRUM FOR THE TIME-DEPENDENT HARMONIC OSCILLATOR WITH A SINGULAR PERTURBATION

2007 ◽  
Vol 21 (10) ◽  
pp. 585-593 ◽  
Author(s):  
JEONG RYEOL CHOI ◽  
JUN-YOUNG OH
Keyword(s):  
Singular Perturbation ◽  
Harmonic Oscillator ◽  
Continuous Spectrum ◽  
Unitary Operator ◽  
Energy Eigenvalue ◽  
Invariant Operator ◽  
Quantum States ◽  
Wave Functions ◽  
Time Dependent ◽  
Discrete Energy

The quantum states with continuous spectrum for the time-dependent harmonic oscillator perturbed by a singularity are investigated. This system does not oscillate while the system that has discrete energy eigenvalue does. Exact wave functions satisfying the Schrödinger equation for the system are derived using invariant operator and unitary operator together.

GEOMETRIC PHASES, SQUEEZED QUANTUM STATES AND GAUSSIAN WAVE PACKET STATES OF RELIC GRAVITONS

2012 ◽  
Vol 18 ◽  
pp. 13-17
Author(s):  
K. BAKKE ◽  
I. A. PEDROSA ◽  
C. FURTADO
Keyword(s):  
Wave Packet ◽  
Linear Time ◽  
Invariant Operator ◽  
Quantum States ◽  
Time Dependent ◽  
Gaussian Wave Packet ◽  
Geometric Phases ◽  
Uncertainty Product ◽  
Quantized Field ◽  
Generalized Time

In this contribution, we discuss quantum effects on relic gravitons described by the Friedmann-Robertson-Walker (FRW) spacetime background by reducing the problem to that of a generalized time-dependent harmonic oscillator, and find the corresponding Schrödinger states with the help of the dynamical invariant method. Then, by considering a quadratic time-dependent invariant operator, we show that we can obtain the geometric phases and squeezed quantum states for this system. Furthermore, we also show that we can construct Gaussian wave packet states by considering a linear time-dependent invariant operator. In both cases, we also discuss the uncertainty product for each mode of the quantized field.

EXACT QUANTUM STATES OF AN INVERTED PENDULUM UNDER TIME-DEPENDENT GRAVITATION

2004 ◽  
Vol 19 (24) ◽  
pp. 4165-4172 ◽  
Author(s):  
I. A. PEDROSA ◽  
I. GUEDES
Keyword(s):  
Exact Solutions ◽  
Inverted Pendulum ◽  
Quantum States ◽  
Wave Functions ◽  
Time Dependent ◽  
Invariant Method ◽  
Exact Quantum ◽  
Generalized Time

We discuss the Lewis and Riesenfeld invariant method for cases where the invariant has continuous eigenvalues and use it to find the Schrödinger wave functions of an inverted pendulum under time-dependent gravitation. As a particular case, we consider an inverted pendulum with exponentially increasing mass and constant gravitation. We also obtain the exact solutions for a generalized time-dependent inverted pendulum.

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.

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.

NEW NONCLASSICAL SOLUTION ON GENERALIZED PAUL TRAP TYPE: NONCLASSICAL STUDY

2000 ◽  
Vol 15 (16) ◽  
pp. 1071-1078
Author(s):  
BISWANATH RATH
Keyword(s):  
Energy Level ◽  
Harmonic Oscillator ◽  
Annihilation Operator ◽  
Paul Trap ◽  
Simple Expression ◽  
Creation Operator ◽  
Time Dependent ◽  
Dependent Frequency ◽  
Generalized Time

New nonclassical solutions for the harmonic oscillator with generalized time-dependent frequency have been found. Simple expression on energy level, creation operator a†(t) and annihilation operator a(t) have been obtained. Using new solutions we want to show how to study squeezing.

Sign in / Sign up

Export Citation Format

Share Document