Classical orbits from the wave function in the large-quantum-number limit

2003 ◽  
Vol 81 (7) ◽  
pp. 929-939
Author(s):  
James D Bonnar ◽  
Jeffrey R Schmidt
Keyword(s):  
Wave Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Quantum Number ◽  
Coulomb Potential ◽  
Correspondence Principle ◽  
Classical Mechanics ◽  
Classical Trajectories ◽  
Large Quantum ◽  
Large Quantum Number

Classical trajectories for the Coulomb potential are obtained from the large principle quantum-number limit of solutions to the nonrelativistic Schrödinger equation, by use of integral equations satisfied by the radial probability density function. These trajectories are found to be in excellent agreement with those computed directly from classical mechanics, in accordance with a statement of the Bohr Correspondence principle, except in a region very close to the center of force. PACS No.: 05.45.Mt

scholarly journals Selected topics in the large quantum number expansion

2021 ◽  
Author(s):  
Luis Alvarez-Gaume ◽  
Domenico Orlando ◽  
Susanne Reffert
Keyword(s):  
Quantum Number ◽  
Large Quantum ◽  
Large Quantum Number

scholarly journals WAVE FUNCTION TO PARTITION FUNCTION: A CORRELATION

2021 ◽  
Author(s):  
JAYDIP DATTA
Keyword(s):  
Wave Function ◽  
Partition Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Statistical Thermodynamics ◽  
Mathematical Probability ◽  
Function Correlation

In this note the statistical thermodynamics is correlated to wave function through mathematical probability. The note can be subdivided into two following portions.STATISTICS -THE BASIC OF STATISTICAL THERMODYNAMICS: A CORRELATION and PROBABILITY -A THE BASICS OF WAVE FUNCTION .Randomisation , Wave Function , Probability Density Function , Multiplicative Probability , Partition function , Correlation ( K.P ) coefficient , Probability , Weights , Stirring’s Approximation

PROBABILITY: A NOTE

2020 ◽  
Author(s):  
JAYDIP DATTA
Keyword(s):  
Wave Function ◽  
Partition Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Probabilistic Approach ◽  
Wave Functions ◽  
P Wave ◽  
Multiplicative Rule

Wave Function , Probability Density Function , Multiplicative Probability , Partition function .In this note we correlate a quantum normalized probabilistic approach with Algebric approach of Probability . The Probability Density [ Shi ]^2 may be equated as additive wave functions ie [Shi A] +[ Shi B ] . In real probability algebra we also know that P(A) +P(B )= P ( A*B ) . This is termed as multiplicative rule of Probability . Greater is P ( A*B ) = [ Shi ] ^2 greater will be the Probability Density F( x ) .

A QUANTUM-CLASSICAL APPROACH TO MOLECULAR DYNAMICS

2003 ◽  
Vol 02 (01) ◽  
pp. 73-90 ◽  
Author(s):  
G. D. BILLING
Keyword(s):  
Wave Function ◽  
Classical Mechanics ◽  
Basis Set ◽  
Discrete Variable ◽  
Discrete Variable Representation ◽  
Molecular Systems ◽  
Order Expansion ◽  
Classical Trajectories ◽  
Grid Points ◽  
Variable Representation

We present a new method for treating the dynamics of molecular systems. The method has been named "quantum dressed" classical mechanics and is based on an expansion of the wave function in a time-dependent basis-set, the Gauss–Hermite basis-set. From here it is possible to proceed in two ways, one is in principle exact and the other approximate. In the exact approach one constructs a discrete variable representation (DVR) in which the grid points are defined by the Hermite part of the Gauss–Hermite basis set. In the approximate method a second order expansion of the potential around the classical trajectories is introduced and the quantum dymamics solved in a second quantization rather than a wave-function representation.

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