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AIP conference proceedings

On the Quantum Potential and Pulsating Wave Packet in the Harmonic Oscillator

Daniel M. Dubois, Daniel M. Dubois

Published Jan 1, 2008• 0 citations
Publisher
DOI
10.1063/1.3020650

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By solving exactly the time dependent Schrdinger equation for simple harmonic oscillator, we have obtained respectively the wave packet solutions associated with the displaced ground state and the displaced excited eigenstates, and then demonstrated the centroid of the wave packet oscillates according to the classical law and that the wave packet form remains unchanged. For simple harmonic oscillator with the force constant depending on time the wave packets with the same structures as that of the usual simple harmonic oscillator can still be found to move in such a way that the centroids move according to the classical law, but their wave packets may deform in time. Depending on how the force constant varies with time, the wave packets can spread, contract or pulsate.