S. Takagi
Abstract
It is shown that a time-dependent scaling of space and time coordinates transforms the time-dependent Schrödinger equation for a (time-dependent) harmonic oscillator to that for a free particle. This equivalence gives a particularly straightforward way to compute the Feynman kernel. Other applications are also suggested.
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It is shown that a time-dependent scaling of space and time coordinates transforms the time-dependent Schrödinger equation for a (time-dependent) harmonic oscillator to that for a free particle. This equivalence gives a particularly straightforward way to compute the Feynman kernel. Other applications are also suggested.
Key concepts: Physics, Harmonic oscillator, Free particle, Equivalence (formal languages), Feynman diagram, Scaling, Kernel (algebra), Classical mechanics