相关论文: Time as a quantum observable
In this work we will advance farther along a line previously developed concerning our proposal of a time interval operator, on finite dimensional spaces. The time interval operator is Hermitian, and its eigenvalues are time values with a…
It is shown that in presence of certain external fields a well defined self-adjoint time operator exists, satisfying the standard canonical commutation relations with the Hamiltonian. Examples include uniform electric and gravitational…
The classical Hilbert space formulation of the axioms of Quantum Mechanics appears to leave open the question whether the Hermitian operators which are associated with the observables of a finite non-relativistic quantum system are uniquely…
Textbook quantum mechanics treats time as a classical parameter, and not as a quantum observable with an associated Hermitian operator. For this reason, to make sense of usual time-energy uncertainty relations such as $\Delta {t}\Delta…
An apparent paradox is resolved that concerns the existence of time operators which have been derived for the quantum harmonic oscillator. There is an apparent paradox because, although a time operator is canonically conjugate to the…
A self-adjoint operator with dimensions of time is explicitly constructed, and it is shown that its complete and orthonormal set of eigenstates can be used to define consistently a probability distribution of the time of arrival at a…
Bohmian mechnaics is the most naively obvious embedding imaginable of Schr\"odingers's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at…
Some notes and questions about the concept of time are exposed. Particular reference is given to the problem in quantum mechanics, in connection with the indeterminacy principle.
We investigate some spectral properties of time operators which are obtained through Canonical Commutation Relation (CCR) and Positive Operator Valued Measure (POVM) of quantum physics. In addition, we re-interpret the spectral properties…
Time in relativity theory has a status different from that adopted by standard quantum mechanics, where time is considered as a parameter measured with reference to an external absolute Newtonian frame. This status strongly restricts its…
We address the multiplicity of solutions to the time-energy canonical commutation relation for a given Hamiltonian. Specifically, we consider a particle spatially confined in a potential free interval, where it is known that two distinct…
The nonrelativistic Schroedinger equation for motion of a structureless particle in four-dimensional space-time entails a well-known expression for the conserved four-vector field of local probability density and current that are associated…
Time plays a crucial role in the intuitive understanding of the world around us. Within quantum mechanics, however, time is not usually treated as an observable quantity; it enters merely as a parameter in the laws of motion of physical…
In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum…
We construct an effective commutative Schr\"odinger equation in Moyal space-time in $(1+1)$-dimension where both $t$ and $x$ are operator-valued and satisfy $\left[ \hat{t}, \hat{x} \right] = i \theta$. Beginning with a time-reparametrised…
A non-Hermitian operator $H$ defined in a Hilbert space with inner product $\langle\cdot|\cdot\rangle$ may serve as the Hamiltonian for a unitary quantum system, if it is $\eta$-pseudo-Hermitian for a metric operator (positive-definite…
Different quantum mechanical operators can correspond to the same classical quantity. Hermitian operators differing only by operator ordering of the canonical coordinates and momenta at one moment of time are the most familiar example.…
It has been argued that it is incompatible to maintain unitary time-evolution for time-dependent non-Hermitian Hamiltonians when the metric operator is explicitly time-dependent. We demonstrate here that the time-dependent Dyson equation…
The nature of time in quantum mechanics is closely related to the use of a complex, rather than say real, Hilbert space. This becomes particularly clear when considering quantum field theory in time dependent backgrounds, such as in…
The question of how long a particle takes to pass through a potential barrier is still a controversial topic in quantum mechanics. Arguably, the main theoretical problem in obtaining estimates for measurable times is the fact that…