# Foundations of Quantum Mechanics: Derivation of a dissipative Schrödinger equation from first principles

## Abstract

Dissipation in Quantum Mechanics took some time to become a robust field of investigation after the birth of the field. The main issue hindering developments in the field is that the Quantization process was always tightly connected to the Hamiltonian formulation of Classical Mechanics. In this paper we present a quantization process that does not depend upon the Hamiltonian formulation of Classical Mechanics (although still departs from Classical Mechanics) and thus overcome the problem of finding, from first principles, a completely general Schrödinger equation encompassing dissipation. This generalized process of quantization is shown to be nothing but an extension of a more restricted version that is shown to produce the Schrödinger equation for Hamiltonian systems from first principles (even for Hamiltonian velocity dependent potential). - Highlights: • A Quantization process independent of the Hamiltonian formulation of quantum Mechanics is proposed. • This quantization method is applied to dissipative or absorptive systems. • A Dissipative Schrödinger equation is derived from first principles.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22617500

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 380; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CLASSICAL MECHANICS; HAMILTONIANS; QUANTIZATION; QUANTUM MECHANICS; SCHROEDINGER EQUATION

### Citation Formats

```
Gonçalves, L.A., and Olavo, L.S.F., E-mail: olavolsf@gmail.com.
```*Foundations of Quantum Mechanics: Derivation of a dissipative Schrödinger equation from first principles*. United States: N. p., 2017.
Web. doi:10.1016/J.AOP.2017.03.002.

```
Gonçalves, L.A., & Olavo, L.S.F., E-mail: olavolsf@gmail.com.
```*Foundations of Quantum Mechanics: Derivation of a dissipative Schrödinger equation from first principles*. United States. doi:10.1016/J.AOP.2017.03.002.

```
Gonçalves, L.A., and Olavo, L.S.F., E-mail: olavolsf@gmail.com. Mon .
"Foundations of Quantum Mechanics: Derivation of a dissipative Schrödinger equation from first principles". United States.
doi:10.1016/J.AOP.2017.03.002.
```

```
@article{osti_22617500,
```

title = {Foundations of Quantum Mechanics: Derivation of a dissipative Schrödinger equation from first principles},

author = {Gonçalves, L.A. and Olavo, L.S.F., E-mail: olavolsf@gmail.com},

abstractNote = {Dissipation in Quantum Mechanics took some time to become a robust field of investigation after the birth of the field. The main issue hindering developments in the field is that the Quantization process was always tightly connected to the Hamiltonian formulation of Classical Mechanics. In this paper we present a quantization process that does not depend upon the Hamiltonian formulation of Classical Mechanics (although still departs from Classical Mechanics) and thus overcome the problem of finding, from first principles, a completely general Schrödinger equation encompassing dissipation. This generalized process of quantization is shown to be nothing but an extension of a more restricted version that is shown to produce the Schrödinger equation for Hamiltonian systems from first principles (even for Hamiltonian velocity dependent potential). - Highlights: • A Quantization process independent of the Hamiltonian formulation of quantum Mechanics is proposed. • This quantization method is applied to dissipative or absorptive systems. • A Dissipative Schrödinger equation is derived from first principles.},

doi = {10.1016/J.AOP.2017.03.002},

journal = {Annals of Physics},

number = ,

volume = 380,

place = {United States},

year = {Mon May 15 00:00:00 EDT 2017},

month = {Mon May 15 00:00:00 EDT 2017}

}