The symmetry group of the quantum harmonic oscillator in an electric field

• Authors: Juan Lejarreta , Jose Cerveró
• Languages of publication: EN

Abstracts

EN

In this paper we present two results. First, we derive the most general group of infinitesimal transformations for the Schrödinger Equation of the general time-dependent Harmonic Oscillator in an electric field. The infinitesimal generators and the commutation rules of this group are presented and the group structure is identified. From here it is easy to construct a set of unitary operators that transform the general Hamiltonian to a much simpler form. The relationship between squeezing and dynamical symmetries is also stressed. The second result concerns the application of these group transformations to obtain solutions of the Schrödinger equation in a time-dependent potential. These solutions are believed to be useful for describing particles confined in boxes with moving boundaries. The motion of the walls is indeed governed by the time-dependent frequency function. The applications of these results to non-rigid quantum dots and tunnelling through fluctuating barriers is also discussed, both in the presence and in the absence of a time-dependent electric field. The differences and similarities between both cases are pointed out.

Keywords

EN

symmetries; Schrödinger equation; moving boundaries

Discipline

• 03.65.Ca: Formalism
• 03.65.Fd: Algebraic methods(see also 02.20.-a Group theory)
• 42.50.-p: Quantum optics(for lasers, see 42.55.-f and 42.60.-v; see also 42.65.-k Nonlinear optics; 03.65.-w Quantum mechanics)

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2008
• Volume: 6
• Issue: 3
• Pages: 671-684

Dates

published

1 - 9 - 2008

online

17 - 7 - 2008

Contributors

author

Juan Lejarreta

• Física Teórica, Facultad de Ciencias, Universidad de Salamanca, 37008, Salamanca, Spain

author

Jose Cerveró

• Física Teórica, Facultad de Ciencias, Universidad de Salamanca, 37008, Salamanca, Spain

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Identifiers

DOI

10.2478/s11534-008-0040-2