Epsilon coherent states with polyanalytic coefficients for the harmonic oscillator
Tóm tắt
We construct a new class of coherent states indexed by points z of the complex plane and depending on two positive parameters m and
$$ \varepsilon >0$$
by replacing the coefficients
$$z^{n}/\sqrt{n!}$$
of the canonical coherent states by polyanalytic functions. These states solve the identity of the states Hilbert space of the harmonic oscillator at the limit
$$\varepsilon \rightarrow 0^{+}$$
and obey a thermal stability property. Their wavefunctions are obtained in a closed form and their associated Bargmann-type transform is also discussed.
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