mm.physics.fock.oscillator_eigenstate

mrmustard.physics.fock.oscillator_eigenstate(q, cutoff)

Harmonic oscillator eigenstate wavefunction psi_n(q) = <n|q>.

Parameters:

• q (Vector) – a vector containing the q points at which the function is evaluated (units of sqrt{hbar})

• cutoff (int) – maximum number of photons

Returns:

a tensor of size len(q)*cutoff. Each entry with index [i, j] represents the eigenstate evaluated

with number of photons i evaluated at position q[j], i.e., psi_i(q_j).

Return type:

Tensor

Details and Conventions

The q-quadrature eigenstates are defined as

\[\psi_n(x) = 1/sqrt[2^n n!](\frac{\omega}{\pi \hbar})^{1/4} \exp{-\frac{\omega}{2\hbar} x^2} H_n(\sqrt{\frac{\omega}{\pi}} x)\]

where \(H_n(x)\) is the (physicists) n-th Hermite polynomial.

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