Related papers: Probability and complex quantum trajectories
It is shown that a normalisable probability density can be defined for the entire complex plane in the modified de Broglie-Bohm quantum mechanics, which gives complex quantum trajectories. This work is in continuation of a previous one that…
Probability is an important question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the…
Complex quantum trajectories, which were first obtained from a modified de Broglie-Bohm quantum mechanics, demonstrate that Born's probability axiom in quantum mechanics originates from dynamics itself. We show that a normalisable…
The existence of precise particle trajectories in any quantum state is accounted for in a consistent way by allowing delocalization of the particle charge. The relativistic mass of the particle remains within a small volume surrounding a…
We introduce a generalized Lagrangian density - involving a non-Hermitian kinetic term - for a quantum particle with the generalized momentum operator. Upon variation of the Lagrangian, we obtain the corresponding Schrodinger equation. The…
We consider the quantum expectation value \mathcal{A}=\<\psi|A|\psi\> of an observable A over the state |\psi\> . We derive the exact probability distribution of \mathcal{A} seen as a random variable when |\psi\> varies over the set of all…
In this article, the following results are obtained: the process of a randomly wandering particle having a size and a continuous trajectory of motion is considered; (b) based on the study of this probabilistic process, a derivation of the…
We introduce a generalized Lagrangian density - involving a non-Hermitian kinetic term - for a quantum particle with the generalized momentum operator. Upon variation of the Lagrangian, we obtain the corresponding Schr\"odinger equation.…
In this paper, a new conserved current for Klein-Gordon equation is derived. It is shown, for $1+1$-dimensions, the first component of this current is non-negative and reduces to $|\phi|^2$ in non-relativistic limit. Therefore, it can be…
Even though the Bohmian trajectories given by integral curves of the conserved Klein-Gordon current may involve motions backwards in time, the natural relativistic probability density of particle positions is well-defined. The Bohmian…
Recent years have seen increased interest in complexified Bohmian mechanical trajectory calculations for quantum systems, both as a pedagogical and computational tool. In the latter context, it is essential that trajectories satisfy…
The major conceptual difficulties of quantum mechanics are analyzed. They are: the notion "wave-particle", the probabilistic interpretation of the Schroedinger wave \psi-function and hence the probability amplitude and its phase, long-range…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
Maintaining the position that the wave function $\psi$ provides a complete description of state, the traditional formalism of quantum mechanics is augmented by introducing continuous trajectories for particles which are sample paths of a…
A simple relativistic quantum hidden-variable theory of particle trajectories, similar to the Bohm theory but without nonlocal forces between the particles, is proposed. To provide compatibility with statistical predictions of quantum…
The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be non-negative and the integral of them over an entire hypersurface should be equal to one. To satisfy these…
The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex…
The motion of a particle is studied in a random space-time. It is assumed that the velocity is small enough for the non-relativistic approximation to be valid. The randomness of the metric induces a diffusion in coordinate space. Hence it…
The Born probability measure describes the statistics of measurements in which observers self-locate themselves in some region of reality. In $\psi$-ontic quantum theories, reality is directly represented by the wavefunction. We show that…
Within Bohm`s interpretation of quantum mechanics particles follow classical trajectories that are determined by the full solution of the time dependent Schroedinger equation. If this interpretation is consistent it must be possible to…