Computer Simulation of Quantum Phenomena
A new procedure, called the particle method, for the solution of the time-dependent Schrödinger equation is described. It uses the amplitude and phase of the complex wave function, and thus avoids some of the oscillatory problems encountered when the real and imaginary parts of this function are employed. The choice of dependent variables leads to the hydrodynamic analogy to quantum mechanics and the method is close in spirit to computation techniques for classical mechanics. Two examples of the method are presented. The first treats wave-packet dynamics on a two-dimensional quadratic barrier; the second involves proton tunneling in a hydrogen-bonded material.
KeywordsSaddle Point Wave Packet Particle Method Quantum Phenomenon Wigner Distribution
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