Computational Modeling and Visualization of Physical Systems with Python

Chapter 8

Time-dependent quantum mechanics

Can a particle be at two places simultaneously? Could a cat be dead and alive at the same time? If we asked these questions in previous chapters on classical physics, the answer would seem to be obviously silly. However, in the context of quantum physics, the answer is neither obvious nor as silly as it may seem. Enter the fascinating world of quantum physics at the atomic scale where classical physics breaks down, and where few classical beings like us really have any intuitive experience. Even now, quantum mechanics is still somewhat mysterious, though its validity bas been confirmed by available experiments for almost a century since its firm establishment.

The student of classical physics begins by studying motion. To gain a feel for quantum physics, it is important that we also begin with motion in the quantum world. What is free fall motion like in quantum mechanics? How about a simple harmonic oscillator? By studying, simulating, and observing motion in quantum physics, we begin to build up intuition and to understand the conceptual underpinning of quantum mechanics. This may be done even without prior knowledge of quantum mechanics, at least for Sections 8.2 and 8.3, if we treat the Schrödinger equation that governs the quantum world as just a wave equation analogous to wave motion discussed in Section 6.5.

But, quantum motion is not as direct or as easy to study as classical motion. The Schrödinger equation is a partial differential ...