Nonstandard Feynman Path Integral for the Harmonic Oscillator
نویسنده
چکیده
Using Nonstandard Analysis, we will provide a rigorous computation for the harmonic oscillator Feynman path integral. The computation will be done without having prior knowledge of the classical path. We will see that properties of classical physics falls out naturally from a purely quantum mechanical point of view. We will assume that the reader is familiar with Nonstandard Analysis.
منابع مشابه
A Rigorous Real Time Feynman Path Integral and Propagator
Abstract. We will derive a rigorous real time propagator for the Non-relativistic Quantum Mechanic L transition probability amplitude and for the Non-relativistic wave function. The propagator will be explicitly given in terms of the time evolution operator. The derivation will be for all self-adjoint nonvector potential Hamiltonians. For systems with potential that carries at most a finite num...
متن کاملar X iv : q ua nt - p h / 02 11 10 6 v 1 1 8 N ov 2 00 2 Harmonic Oscillator , Coherent States , and Feynman Path Integral
The Feynman path integral for the generalized harmonic oscillator is reviewed, and it is shown that the path integral can be used to find a complete set of wave functions for the oscillator. Harmonic oscillators with different (time-dependent) parameters can be related through unitary transformations. The existence of generalized coherent states for a simple harmonic oscillator can then be inte...
متن کاملExtended Feynman Formula for the Harmonic Oscillator by the Discrete Time Method
We calculate the Feynman formula for the harmonic oscillator beyond and at caustics by the discrete formulation of path integral. The extension has been made by some authors, however, it is not obtained by the method which we consider the most reliable regularization of path integral. It is shown that this method leads to the result with, especially at caustics, more rigorous derivation than pr...
متن کاملA Rigorous Real Time Feynman Path Integral
where φ, ψ ∈ L, H = −~ 2m ∆+V (~x) is essentially self-adjoint, H̄ is the closure ofH , and φ, ψ, V each carries at most a finite number of singularities and discontinuities. In flavor of physics literature, we will formulate the Feynman path integral with improper Riemann integrals. In hope that with further research we can formulate a rigorous polygonal path integral, we will also provide a No...
متن کاملThe Maslov correction in the semiclassical Feynman integral
The Maslov correction to the wave function is the jump of −π/2 in the phase when the system passes through a caustic point. This phenomenon is related to the second variation and to the geometry of paths, as conveniently explained in Feynman’s path integral framework. The results can be extended to any system using the semiclassical approximation. The 1-dimensional harmonic oscillator is used t...
متن کامل