Bohmian trajectories have been used for various purposes, including the numerical simulation of the time-dependent Schrödinger equation and the visualization of time-dependent wave functions. We review the purpose they were invented for: to serve as the foundation of quantum mechanics, i.e., to explain quantum mechanics in terms of a theory that is free of paradoxes and allows an understanding ...

There are only a few analytic solutions available for this partial differential equation. Schrödinger found all of the most useful ones in his first paper on Quantum Mechanics: the Coulomb potential and the harmonic oscillator potential. He published the solution to the nonrelativistic Coulomb problem in his first Wave Mechanics paper but solved the relativistic problem six months earlier. He a...

We constructed the pp-wave limit of N = 4 superconformal mechanics with the off-shell (3,4,1) multiplet. We present the superfield and the component actions which exhibit the interesting property that the interaction parts are completely fixed by the symmetry. We also explicitly demonstrate that the passing to the pp-wave limit can be achieved by keeping at most quadratic nonlinearities in the ...

We all physicist have long been believed that an elementary particle is a wave as well as a particle, but we discuss in this paper that an electron (probably all fermions) is always a particle. Author claim that quantum mechanics (QM) is not such mysterious as Bohr stated that the wave turn to the particle by observation. We can understand QM by natural human sense. The wave nature of electrons...

Three qRules governing wave collapse are given in this paper that provide a foundation theory of quantum mechanics. They are empirical regularities that are known to be valid in macroscopic situations. When projected theoretically into the microscopic domain they predict a novel ontology, including the frequent collapse of atomic wave functions. Future experiments can potentially discriminate b...

I am concerned with two views of quantum mechanics that John S. Bell called " unromantic " : spontaneous wave function collapse and Bohmian mechanics. I discuss some of their merits and report about recent progress concerning extensions to quantum field theory and relativity. In the last section, I speculate about an extension of Bohmian mechanics to quantum gravity.

Hugh Everett III presented pure wave mechanics, sometimes referred to as the many-worlds interpretation, as a solution to the quantum measurement problem. While pure wave mechanics is a deterministic physical theory with no probabilities, Everett sought to show how the theory might be understood as making the standard quantum statistical predictions as appearances to observers who were themselv...

Zufiria’s higher-order Boussinesq type equations are studied by transforming them into solvable ordinary differential equations. Various families of their travelling wave solutions are generated, which include periodic wave, solitary wave, periodic-like wave, solitonlike wave, Jacobi elliptic function periodic wave, combined non-degenerative Jacobi elliptic function-like wave, Weierstrass ellip...