Abstract
The time evolution of a quantum system is governed by the time-dependent Schrödinger equation. In a first computer experiment a particle in a one-dimensional potential well is simulated. We use a combination of implicit and explicit methods which implies a unitary transformation and conserves the norm of the wavefunction. Next we consider systems which can be described sufficiently accurate by a linear combination of a finite number of basis states. The Schrödinger equation is solved numerically with the popular fourth order Runge–Kutta method. In several computer experiments we study a two-level system with constant or time-dependent interaction. Relaxation terms are included within the density matrix formalism leading to the Bloch equations which are relevant not only to NMR experiments but also to describe dephasing of a quantum bit. The resonance curve and its dependence on intensity are studied as well as inversion of a quantum bit by an external pulse. Further experiments deal with the ladder model for exponential decay and the Landau–Zener model for electronic transitions during slow collisions.
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© 2010 Springer-Verlag Berlin Heidelberg
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Scherer, P.O. (2010). Simple Quantum Systems. In: Computational Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13990-1_19
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DOI: https://doi.org/10.1007/978-3-642-13990-1_19
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Online ISBN: 978-3-642-13990-1
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