A no-go result for the quantum damped harmonic oscillator

Abstract

In this letter we show that it is not possible to set up a canonical quantization for the damped harmonic oscillator using the Bateman lagrangian. In particular, we prove that no square integrable vacuum exists for the {\em natural} ladder operators of the system, and that the only vacua can be found as distributions. This implies that the procedure proposed by some authors is only formally correct, and requires a much deeper analysis to be made rigorous.

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Cited by in corpus (11)

• Weak pseudo-bosons
• Bateman Oscillators: Caldirola-Kanai and Null Lagrangians and Gauge Functions
• A new approach to the quantization of the damped harmonic oscillator
• Susy for non-Hermitian Hamiltonians, with a view to coherent states
• Quantization of nonlinear non-Hamiltonian systems
• Square-integrable eigenfunctions in quantizing the Bateman oscillator model
• Multiplication of distributions in a linear gain and loss system
• Algebraic analysis of non-Hermitian quadratic Hamiltonians
• Poisson bracket operator
• Classical Hamiltonian Systems with Balanced loss and gain
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