Part II: Time-Dependent Perturbation Theory of the infinite Potential Wall

The orthodox interpretation of transitions between quantum states in terms of discontinuous jumps is treated as an adjunct to the Schrödinger equation itself. In the causal interpretation, the particle position and momentum are well-defined and the transition can be described as a continuous evolution of the quantum particle according to the time-dependent Schrödinger equation. To study transitions in a two-level system, time-dependent perturbation theory must be used.
For the particular case of a two-level system perturbed by a periodic external field (but without quantization of the transition-inducing field and ignoring radiation effects), an accurate solution can be derived.
This Demonstration studies a transition from the first state to the fourth excited state and back to the first state.
In the causal interpretation, ensembles of particles are characterized by a wavefunction, an initial position, and a trajectory. The trajectories are streamlines in the Madelung fluid, regarded as paths of quantum particles that are not directly measurable because of the perturbation caused by the measurement process. In the superposition of states, the energy for each individual quantum particle evolves in a continuous manner. The particle's motion evolves such that its energy, depending on its initial position.

In the Bohm interpretation (=causal interpretation) are no quantum jumps.
Reference:
C. Dewdney and M. M. Lam, "What Happens During a Quantum Transition?," Information Dynamics (H. Atmanspacher and H. Scheingraber, eds.), New York: Plenum Press, 1991.
Klaus von Bloh, Causal Interpretation of Transitions in a Two-Level System" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/CausalInterpretationOfTransitionsInATwoLeve...

Programmed by: Klaus von Bloh

Category:

Education

Tags:

• computer science
• David Bohm
• quantum trajectories
• de Broglie interpretation
• perturbation theory
• quantum jumps
• Schrödinger equation
• quantum theory
• hidden variables
• ontological interpretation
• pilot wave theory
• quantum motion
• discrete Schrödinger equation
• quantum potential
• quantum mechanics

[kvb100b]

@LANN98

Thank you for your –email

. I use a Fortran Program to calculate the discrete Schrödinger-function (Crank-Nicolson implicit integration scheme) with a time-dependent potential and Mathematica to display the results

[kvb100b]

could you please explain your video? what program did you use? what do the individual lines represent?