Use of mathematical logical concepts in quantum mechanics: an example

Use of Mathematical Logical Concepts in Quantum Mechanics: An Example

The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has meaning. A simple example of such a system, based on an example described by Smullyan, is studied here. Based on a path interpretation for some word states, def...

Planar Quantum Mechanics: an Intriguing Supersymmetric Example

After setting up a Hamiltonian formulation of planar (matrix) quantum mechanics, we illustrate its effectiveness in a non-trivial supersymmetric example. The numerical and analytical study of two sectors of the model, as a function of ’t Hooft’s coupling λ, reveals both a phase transition at λ = 1 (disappearence of the mass gap and discontinuous jump in Witten’s index) and a new form of strong-...

Mathematical Methods in Quantum Mechanics

Mathematical Techniques in Quantum Mechanics

Mathematical Methods in Quantum Mechanics