共查询到20条相似文献,搜索用时 15 毫秒
1.
We calculate the time taken by a wave packet to travel through a classically forbidden region of space in space fractional quantum mechanics. We obtain the close form expression of tunneling time from a rectangular barrier by stationary phase method. We show that tunneling time depends upon the width b of the barrier for and therefore Hartman effect doesn't exist in space fractional quantum mechanics. Interestingly we found that the tunneling time monotonically reduces with increasing b. The tunneling time is smaller in space fractional quantum mechanics as compared to the case of standard quantum mechanics. We recover the Hartman effect of standard quantum mechanics as a special case of space fractional quantum mechanics. 相似文献
2.
Manfred Neumann 《Foundations of Physics》1978,8(9-10):721-733
A procedure is given for the transformation of quantum mechanical operator equations into stochastic equations. The stochastic equations reveal a simple correlation between quantum mechanics and classical mechanics: Quantum mechanics operates with “optimal estimations,” classical mechanics is the limit of “complete information.” In this connection, Schrödinger's substitution relationsp x → -i? ?/?x, etc, reveal themselves as exact mathematical transformation formulas. The stochastic version of quantum mechanical equations provides an explanation for the difficulties in correlating quantum mechanics and the theory of relativity: In physics “time” is always thought of as a numerical parameter; but in the present formalism of physics “time” is described by two formally totally different quantities. One of these two “times” is a numerical parameter and the other a random variable. This last concept of time shows all the properties required by the theory of relativity and is therefore to be considered as the relativistic time. 相似文献
3.
《Physics Reports》2002,364(2):83-174
The concepts of time delay and dwell time in quantum mechanics, and their applications to regular and chaotic scattering, to statistical mechanics, and to the tunneling time problem, among others, are reviewed. The emphasis is on physical concepts and on a pedagogical presentation. 相似文献
4.
Time as a Geometric Concept Involving Angular Relations in Classical Mechanics and Quantum Mechanics
Juan?Eduardo?Reluz?Machicote 《Foundations of Physics》2010,40(11):1744-1778
The goal of this paper is to introduce the notion of a four-dimensional time in classical mechanics and in quantum mechanics
as a natural concept related with the angular momentum. The four-dimensional time is a consequence of the geometrical relation
in the particle in a given plane defined by the angular momentum. A quaternion is the mathematical entity that gives the correct
direction to the four-dimensional time. 相似文献
5.
An investigation of two-time correlation functions is reported
within the framework of (i) stochastic quantum mechanics and (ii)
conventional Heisenberg-Schr?dinger quantum mechanics. The
spectral functions associated with the two-time electric dipole moment
correlation functions are worked out in detail for the case of the
hydrogen atom. While the single time averages are identical for
stochastic and conventional quantum mechanics, differences arise in
the two approaches for multiple time correlation functions. 相似文献
6.
We use Padoa's principle of independence of primitive symbols in axiomatic systems in order to discuss the mathematical role of time and spacetime in some classical physical theories. We show that time is eliminable in Newtonian mechanics and that spacetime is also dispensable in Hamiltonian mechanics, Maxwell's electromagnetic theory, the Dirac electron, classical gauge fields, and general relativity. 相似文献
7.
In the discourse of quantum mechanics it is usual to say that non-commuting observables cannot have definite values at the same time, or that they cannot be simultaneously measured. But, what does the term ‘cannot’ mean in this context? Does it stand for impossible? Should Heisenberg’s principle be read in terms of uncertainty or of indeterminacy? On the other hand, whereas the debates about the nature of time in classical and relativistic mechanics have been many and varied, the question about the nature of time in quantum mechanics has not received the same attention, especially when compared to the large amount of literature on interpretive issues. The purpose of this paper is to show that, under a realist interpretation of quantum mechanics, these two matters, possibility and time, are strongly related. The final aim is to argue that, when possibility and actuality are conceived as irreducible modes of being, they are correlated to two different notions of time that can be distinguished in the quantum realm: parameter-time and event-time. 相似文献
8.
Agung Budiyono 《International Journal of Theoretical Physics》2014,53(4):1276-1298
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of local causality. By contrast, here we shall show that the Schrödinger equation with Born’s statistical interpretation of wave function and uncertainty relation can be derived from a statistical model of microscopic stochastic deviation from classical mechanics which is selected uniquely, up to a free parameter, by the principle of Local Causality. Quantization is thus argued to be physical and Planck constant acquires an interpretation as the average stochastic deviation from classical mechanics in a microscopic time scale. Unlike canonical quantization, the resulting quantum system always has a definite configuration all the time as in classical mechanics, fluctuating randomly along a continuous trajectory. The average of the relevant physical quantities over the distribution of the configuration are shown to be equal numerically to the quantum mechanical average of the corresponding Hermitian operators over a quantum state. 相似文献
9.
We construct a stochastic mechanics by replacing Bohm‧s first-order ordinary differential equation of motion with a stochastic
differential equation where the stochastic process is defined by the set of Bohmian momentum time histories from an ensemble
of particles. We show that, if the stochastic process is a purely random process with n-th order joint probability density in the form of products of delta functions, then the stochastic mechanics is equivalent
to quantum mechanics in the sense that the former yields the same position probability density as the latter. However, for
a particular non-purely random process, we show that the stochastic mechanics is not equivalent to quantum mechanics. Whether
the equivalence between the stochastic mechanics and quantum mechanics holds for all purely random processes but breaks down for all non-purely random processes remains an open question. 相似文献
10.
Quantum motion of particles tunneling a double barrier potential is considered by using stochastic mechanics. Stochastic-mechanical trajectories give us information about complex motion of tunneling particles that is not obtained within the framework of ordinary quantum mechanics. Using such information, we calculate the tunneling times within each of the barriers which depend on the distance between them. It is found that the stochastic-mechanical tunneling time shows better asymptotic behavior than the quantum-mechanical dwell time and presence time. 相似文献
11.
Recently the possibility was raised that time can be regarded as a dynamical variable. This leads to the formulation of discrete mechanics, with the usual continuum mechanics appearing as an approximation. The difference between these two is examined in this paper. 相似文献
12.
The usual quantum mechanics describes the mass eigenstates. To describe the proper-time eigenstates, a duality theory of the
usual quantum mechanics was developed. The time interval is treated as an operator on an equal footing with the space interval,
and the quantization of the spacetime intervals between events is obtained. As a result, one can show that there exists a
zero-point time interval. 相似文献
13.
14.
Several years ago, in quantum mechanics, Davies proposed a method to calculate particle’s traveling time with the phase difference of wave function. The method is convenient for calculating the sojourn time inside a potential step and the tunneling time through a potential hill. We extend Davies’ non-relativistic calculation to relativistic quantum mechanics, with and without particle-antiparticle creation, using Klein–Gordon equation and Dirac Equation, for different forms of energy-momentum relation. The extension is successful only when the particle and antiparticle creation/annihilation effect is negligible. 相似文献
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17.
Jack Cohn 《International Journal of Theoretical Physics》1983,22(1):19-28
A formulation of nonrelativistic, spinless, quantum mechanics is presented which is based on four postulates. Three of the postulates are very analogous to relations that hold in an operator formulation of classical mechanics, and the fourth is that the wave function evolves linearly in time. The conventional statistical assertions of quantum theory as well as the Schrödinger equation are recovered. 相似文献
18.
Sabine Hossenfelder 《Foundations of Physics》2011,41(9):1521-1531
We propose to experimentally test non-deterministic time evolution in quantum mechanics by consecutive measurements of non-commuting
observables on the same prepared state. While in the standard theory the measurement outcomes are uncorrelated, in a super-deterministic
hidden variables theory the measurements would be correlated. We estimate that for macroscopic experiments the correlation
time is too short to have been noticed yet, but that it may be possible with a suitably designed microscopic experiment to
reach a parameter range where one would expect a super-deterministic modification of quantum mechanics to become relevant. 相似文献
19.
Stefano Pasquero 《Reports on Mathematical Physics》2004,53(1):103-122
A new context is introduced to give a formal geometric environment for the study of impulsive mechanics of systems with finite number of degrees of freedom. The new structures embody the usual ones of analytical mechanics such as tangent bundles for time independent systems and jet-bundles for time dependent ones. They allow a causally consistent definition of active impulse acting on the systems and a clear geometric view of the equations of motion. 相似文献
20.
We analyze the effects of inelastic scattering on the tunneling time theoretically, using generalized Nelson’s quantum mechanics.
This generalization enables us to describe quantum system with channel couplings and optical potential in a real time stochastic
approach, which seems to give us a new insight into quantum mechanics beyond Copenhagen interpretation 相似文献