If a time-dependent Hamiltonian is allowed to evolve adiabatically, and after a cycle, if it returns to its original form, then the ground state wavefunction must have picked up the dynamic or(and) the geometric phase factor(s) due to some interaction during the above evolution. Here, (i) we invoke the Pancharatnam's notion of phase retardation to show that the microscopic origin of Berry's phase is due to a change in the phase velocity (of a wavefunction), and (ii) the dynamic phase factor is shown to have its origin in the group velocity of a wavefunction. We also expose that the emitted photon polarization during an electronic transition has its origin in the changes of the phase velocity of the electron wavefunction.If a time-dependent Hamiltonian is allowed to evolve adiabatically, and after a cycle, if it returns to its original form, then the ground state wavefunction must have picked up the dynamic or(and) the geometric phase factor(s) due to some interaction during the above evolution. Here, (i) we invoke the Pancharatnam's notion of phase retardation to show that the microscopic origin of Berry's phase is due to a change in the phase velocity (of a wavefunction), and (ii) the dynamic phase factor is shown to have its origin in the group velocity of a wavefunction. We also expose that the emitted photon polarization during an electronic transition has its origin in the changes of the phase velocity of the electron wavefunction.

Jan 23, 20130 citations

Properties of Wavefunctions

Brian P. Anderson

SPIE eBooksSep 12, 20190 citations

Wavefunction transformation due to changing group and phase velocities: an expose

Andrew Das Arulsamy

If a time-dependent Hamiltonian is allowed to evolve adiabatically, and if it returns to its original form, then the ground state wavefunction must have picked up the dynamic or(and) the geometric phase factor(s) due to some interaction during the above evolution. Here, (i) we invoke the Pancharatnam's notion of phase retardation to show that the microscopic origin of Berry's phase is due to a change in the phase velocity (of a wavefunction), and (ii) the dynamic phase factor is shown to have its origin in the group velocity of a wavefunction. We also expose that the emitted photon's polarization during an electronic transition has its origin in the changes of the phase velocity of the electron wavefunction. Here, we prove the above statements, (i) and (ii), such that they are not due to some interpretational issues, hence, an expos ${\rm \acute{e}}$ .If a time-dependent Hamiltonian is allowed to evolve adiabatically, and if it returns to its original form, then the ground state wavefunction must have picked up the dynamic or(and) the geometric phase factor(s) due to some interaction during the above evolution. Here, (i) we invoke the Pancharatnam's notion of phase retardation to show that the microscopic origin of Berry's phase is due to a change in the phase velocity (of a wavefunction), and (ii) the dynamic phase factor is shown to have its origin in the group velocity of a wavefunction. We also expose that the emitted photon's polarization during an electronic transition has its origin in the changes of the phase velocity of the electron wavefunction. Here, we prove the above statements, (i) and (ii), such that they are not due to some interpretational issues, hence, an expos${\rm \acute{e}}$.

arXiv:1302.5050Jan 23, 20130 citations

Complex wavefunctions

Tim Freegarde

Cambridge University Press eBooksNov 8, 20120 citations

Properties of Phase Space Wavefunctions and Eigenvalue Equation of Momentum Dispersion Operator

Ravo Tokiniaina Ranaivoson

This paper is a continuation of our previous works about coordinate, momentum, dispersion operators and phase space representation of quantum mechanics. It concerns a study on the properties of wavefunctions in the phase space representation and the momentum dispersion operator, its representations and eigenvalue equation. After the recall of some results from our previous papers, we give most of the main properties of the phase space wavefunctions and consider some examples of them. Then we establish the eigenvalue equation for the differential operator corresponding to the momentum dispersion operator in the phase space representation. It is shown in particular that any phase space wavefunction is solution of this equation.This paper is a continuation of our previous works about coordinate, momentum, dispersion operators and phase space representation of quantum mechanics. It concerns a study on the properties of wavefunctions in the phase space representation and the momentum dispersion operator, its representations and eigenvalue equation. After the recall of some results from our previous papers, we give most of the main properties of the phase space wavefunctions and consider some examples of them. Then we establish the eigenvalue equation for the differential operator corresponding to the momentum dispersion operator in the phase space representation. It is shown in particular that any phase space wavefunction is solution of this equation.

arXiv:1711.07308International Journal of Applied Mathematics and Theoretical PhysicsJan 1, 20181 citation

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