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.

On the dynamics of a time-dependent mesoscopic LC circuit with a negative inductance

2016 ◽  
Vol 30 (12) ◽  
pp. 1650122 ◽  
Author(s):  
I. A. Pedrosa ◽  
E. Nogueira ◽  
I. Guedes
Keyword(s):  
Magnetic Flux ◽  
Wave Packet ◽  
Operator Method ◽  
Invariant Operator ◽  
Time Dependent ◽  
Expectation Values ◽  
Gaussian States ◽  
Faraday’S Law ◽  
Uncertainty Product ◽  
Lc Circuit

We discuss the problem of a mesoscopic LC circuit with a negative inductance ruled by a time-dependent Hermitian Hamiltonian. Classically, we find unusual expressions for the Faraday’s law and for the inductance of a solenoid. Quantum mechanically, we solve exactly the time-dependent Schrödinger equation through the Lewis and Riesenfeld invariant operator method and construct Gaussian wave packet solutions for this time-dependent LC circuit. We also evaluate the expectation values of the charge and the magnetic flux in these Gaussian states, their quantum fluctuations and the corresponding uncertainty product.

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.

Solving Time-dependent Schrödinger Equation Using Gaussian Wave Packet Dynamics

2018 ◽  
Vol 73 (9) ◽  
pp. 1269-1278
Author(s):  
Min-Ho Lee ◽  
Chang Woo Byun ◽  
Nark Nyul Choi ◽  
Dae-Soung Kim
Keyword(s):  
Schrödinger Equation ◽  
Wave Packet ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Gaussian Wave Packet ◽  
Wave Packet Dynamics

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.

Gaussian wave packet states of a generalized inverted harmonic oscillator with time-dependent mass and frequency

2015 ◽  
Vol 93 (8) ◽  
pp. 841-845 ◽  
Author(s):  
I.A. Pedrosa ◽  
Alberes Lopes de Lima ◽  
Alexandre M. de M. Carvalho
Keyword(s):  
Wave Packet ◽  
Harmonic Oscillator ◽  
Uncertainty Relation ◽  
Quantum Correlations ◽  
Wave Functions ◽  
Time Dependent ◽  
Gaussian Wave Packet ◽  
Order Ordinary Differential Equation ◽  
Quantum Invariant ◽  
Dependent Mass

We derive quantum solutions of a generalized inverted or repulsive harmonic oscillator with arbitrary time-dependent mass and frequency using the quantum invariant method and linear invariants, and write its wave functions in terms of solutions of a second-order ordinary differential equation that describes the amplitude of the damped classical inverted oscillator. Afterwards, we construct Gaussian wave packet solutions and calculate the fluctuations in coordinate and momentum, the associated uncertainty relation, and the quantum correlations between coordinate and momentum. As a particular case, we apply our general development to the generalized inverted Caldirola–Kanai oscillator.

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