# Coherent distributions for the rigid rotator

## Abstract

Coherent solutions of the classical Liouville equation for the rigid rotator are presented as positive phase-space distributions localized on the Lagrangian submanifolds of Hamilton-Jacobi theory. These solutions become Wigner-type quasiprobability distributions by a formal discretization of the left-invariant vector fields from their Fourier transform in angular momentum. The results are consistent with the usual quantization of the anisotropic rotator, but the expected value of the Hamiltonian contains a finite “zero point” energy term. It is shown that during the time when a quasiprobability distribution evolves according to the Liouville equation, the related quantum wave function should satisfy the time-dependent Schrödinger equation.

- Authors:

- CP 15-645, Bucharest 014700 (Romania)

- Publication Date:

- OSTI Identifier:
- 22596852

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 6; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANGULAR MOMENTUM; BOLTZMANN-VLASOV EQUATION; FOURIER TRANSFORMATION; HAMILTONIANS; HAMILTON-JACOBI EQUATIONS; LAGRANGIAN FUNCTION; MATHEMATICAL SOLUTIONS; PHASE SPACE; QUANTIZATION; SCHROEDINGER EQUATION; TIME DEPENDENCE; VECTOR FIELDS; WAVE FUNCTIONS

### Citation Formats

```
Grigorescu, Marius.
```*Coherent distributions for the rigid rotator*. United States: N. p., 2016.
Web. doi:10.1063/1.4953369.

```
Grigorescu, Marius.
```*Coherent distributions for the rigid rotator*. United States. doi:10.1063/1.4953369.

```
Grigorescu, Marius. 2016.
"Coherent distributions for the rigid rotator". United States.
doi:10.1063/1.4953369.
```

```
@article{osti_22596852,
```

title = {Coherent distributions for the rigid rotator},

author = {Grigorescu, Marius},

abstractNote = {Coherent solutions of the classical Liouville equation for the rigid rotator are presented as positive phase-space distributions localized on the Lagrangian submanifolds of Hamilton-Jacobi theory. These solutions become Wigner-type quasiprobability distributions by a formal discretization of the left-invariant vector fields from their Fourier transform in angular momentum. The results are consistent with the usual quantization of the anisotropic rotator, but the expected value of the Hamiltonian contains a finite “zero point” energy term. It is shown that during the time when a quasiprobability distribution evolves according to the Liouville equation, the related quantum wave function should satisfy the time-dependent Schrödinger equation.},

doi = {10.1063/1.4953369},

journal = {Journal of Mathematical Physics},

number = 6,

volume = 57,

place = {United States},

year = 2016,

month = 6

}