# Time dependence in quantum mechanics

@article{Briggs2000TimeDI, title={Time dependence in quantum mechanics}, author={John S. Briggs and Jan Michael Rost}, journal={The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics}, year={2000}, volume={10}, pages={311-318} }

Abstract:It is shown that the time-dependent equations (Schrödinger and Dirac) for a quantum system can be derived from the time-independent equation for the larger object of the system interacting with its environment, in the limit that the dynamical variables of the environment can be treated semiclassically. The time which describes the quantum evolution is then provided parametrically by the classical evolution of the environment variables. The method used is a generalization of that known…

## 35 Citations

### On the problem of time in quantum mechanics

- Physics
- 2017

The problem of time in quantum mechanics (QM) concerns the fact that in the Schrödinger equation time is a parameter, not an operator. Pauli's objection to a time–energy uncertainty relation analogue…

### Conditional interpretation of time in quantum gravity and a time operator in relativistic quantum mechanics

- Physics
- 2020

The problem of time in the quantization of gravity arises from the fact that time in Schrödinger’s equation is a parameter. This sets time apart from the spatial coordinates, represented by operators…

### The derivation of time-dependent Schrödinger equations

- Physics
- 2007

Beginning with an entangled state of a time-independent (TI) quantum system coupled to its TI quantum environment, we show that a time-dependent Schrödinger equation (TDSE) for the quantum system…

### A dynamical time operator in relativistic quantum mechanics

- Physics
- 2009

A self-adjoint dynamical time operator is introduced in Dirac’s relativistic formulation of quantum mechanics and shown to satisfy with the Hamiltonian a commutation relation analogous to that of the…

### Time-Dependent Quantum Theory

- Physics
- 2013

In this chapter, we continue laying the foundations for the later chapters by reviewing some basic properties of the time-dependent Schrodinger equation and the corresponding time-evolution operator,…

### Dynamical stabilization and time in open quantum systems

- Physics
- 2013

The meaning of time in an open quantum system is considered under the assumption that both, system and environment, are quantum mechanical objects. The Hamilton operator of the system is…

### Classical limit of the interaction of a quantum system with the electromagnetic field

- Physics
- 2004

The interaction of nonrelativistic matter with the quantized electromagnetic field is investigated in the classical limit of large photon numbers. Quantization of both matter, say an atom, and the…

### Variational principle for mixed classical–quantum systems

- Physics
- 2007

An extended variational principle providing the equations of motion for a system consisting of interacting classical, quasiclassical, and quantum components is presented, and applied to the model of…

### Time in quantum mechanics: A fresh look at the continuity equation

- PhysicsPhysical Review A
- 2018

The local conservation of a physical quantity whose distribution changes with time is mathematically described by the continuity equation. The corresponding time parameter, however, is defined with…

### On the Quantum-Classical Character of the Quantum Wavefunction of Material Particles

- Physics
- 2006

We show that the quantum wavefunction, interpreted as the probability density of finding a single non-localized quantum particle, which evolves according to classical laws of motion, is an…

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