Interpretation Of Wave Function Research Articles

Solvable relativistic quantum dots with vibrational spectra

For Klein-Gordon equation a consistent physical interpretation of wave functions is reviewed as based on a proper modification of the scalar product in Hilbert space. Bound states are then studied in a deep-square-well model where the spectrum is roughly equidistant and where a fine-tuning of the levels is mediated by $$\mathcal{P}\mathcal{T}$$ -symmetric interactions (composed of imaginary delta functions) which mimic creation/annihilation processes.

Schrödinger's Equation and Classical Brownian Motion

In the context of quantum mechanics, Schrodinger's equation has many possible interpretations, none of which appear to be entirely satisfactory. One reason for this is that there is no known microscopic model which yields both Schrodinger's equation and an accompanying ‘sensible’ interpretation. In contrast to this the diffusion equation is well known as a phenomenological equation obtainable from the microscopic model of Brownian motion. In this case the microscopic model provides an unambiguous interpretation of the partial differential equation. In this article we review work which shows that Schrodinger's equation by itself is also easily obtained from a lattice random walk version of the Brownian motion model. In this system, Schrodinger's equation arises by projection and the interpretation of wave functions is as direct and unambiguous as the interpretation of density in the diffusion case. However the direct interpretation is compatible with quantum mechanics only in a statistical sense in the context of ensembles of particles. This shows that measurement theory is the aspect of quantum theory which harbours the problems of interpretation, and we suggest the study of this and related systems to clearly illuminate the boundary between dynamics and measurement.

Internal structures of electrons and photons: The concept of extended particles revisited

The theoretical foundations of quantum mechanics and de Broglie–Bohm mechanics are analyzed and it is shown that both theories employ a formal approach to microphysics. By using a realistic approach it can be established that the internal structures of extended particles comply with a wave equation. Including external potentials yields the Schrödinger equation in this context, is arbitrary due to internal energy components. The statistical interpretation of wave functions in quantum theory as well as Heisenberg’s uncertainty relations are shown to be an expression of this, fundamental arbitrariness. Electrons and photons can be described by an identical formalism, providing formulations equivalent to the Maxwell equations. Electrostatic interactions justify the initial assumption of electron–wave stability: the stability of electron waves can be referred to vanishing intrinsic fields of interaction. The theory finally points out some fundamental difficulties for a fully covariant formulation of quantum electrodynamics, which seem to be related to the existing infinity problems in this field.

A limit theorem for p-adic-valued probability distributions

Probability models in which probabilities, defined in the sense of von Mises as limits of relative frequencies, can belong to p-adic number fields appeared in connection with the problem of the probabilistic interpretation of wave functions in p-adic-valued quantum mechanics and field theory. Here we present a variant of axiomatic p-adic probability theory in the framework of the theory of analytic distributions on p-adic spaces. We prove a theorem on the existence of p-adic-valued probability distributions on p-adic sequences and obtain a limit theorem for sums of independent random variables (an analogue of the law of large numbers).

STOCHASTIC INFLATION AND QUANTUM COSMOLOGY

We review stochastic inflation and its consequences for the interpretation of wave functions in quantum cosmology.

The Analysis and Understanding of Ionisation Phenomena: Ab initio Molecular Wavefunctions

Two distinctly different kinds of information can be obtained from ab initio wavefunctions. The v~lue of observables can be computed, quite accurately for relatively small systems, but this only complements experiment. However, the analysis and interpretation of wavefunctions can lead to conceptual understanding of the significance of measured values. Ab initio wavefunctions are essential because they provide a unique and sound basis for determining the importance of various mechanisms. Three cases where this analysis has lead to new understanding will be described. The shift to higher binding energy (BE) of the 50" orbital relative to the hr orbital for chemisorbed CO is shown to be dominantly an electrostatic effect; it does not indicate the chemical bonding. The shift of core level BEs with the size of metal clusters is shown to be an initial state effect which depends on the coordination of the ionised atom; differential final state effects may not be large. The satellite structure for core ionisation of the NO dimer is due to both intra- and inter-unit screening. In all� these cases, the correct mechanisms could only be established with accurate ab initio wavefunctions.

Extended space-time and the interpretation of wave functions

An extension of space and time is presented whereby a point particle can oscillate into the immediate past and future. Rapid oscillation implies that the particle is seen at, or represented over, each point in time a large number of times, each representation being associated with a different phase of the oscillation. Each cycle gives rise to an unavoidable drift from the particle's original position and hence the particle representations are scattered about the original position. Many such models of particle dynamics are possible and have implications for the interpretation of quantum mechanics and the conception of nonrealistic, nonlocal theories.

Macroscopic Bodies in Quantum Theory

It is shown that if the wave function of a massive body is $\ensuremath{\psi}=\ensuremath{\Sigma}{c}_{n}{\ensuremath{\psi}}_{n}$, where the ${\ensuremath{\psi}}_{n}$ are macroscopically distinguishable states, then the observation of interferences between the various ${\ensuremath{\psi}}_{n}$ requires inconceivable laboratory conditions (e.g., the experiment may last longer than the lifetime of the universe). It is therefore proposed to interpret $\ensuremath{\Sigma}{c}_{n}{\ensuremath{\psi}}_{n}$ as a mixture of states, and not as a superposition. This new interpretation of wave functions is consistent with experience and is free from the paradoxical features of the "orthodox" measurement theory.

Detection of Particles inside Potential Barriers

THERE appears to be some uncertainty regarding the interpretation of wave functions in classically inaccessible regions, where the total energy is less than the potential energy. The following question is asked often : Can one detect a particle inside a barrier without giving it enough energy to be, classically, in the region of localization?