 Cartesian number state of the three-dimensional isotropic harmonic oscillator

ID: cartesian-number-state-of-the-three-dimensional-isotropic-harmonic-oscillator

From the normalized ground state annihilated by every

A_{i}

, the normalized Cartesian number states are

∣ n_{1}, n_{2}, n_{3} ⟩ = \prod_{i = 1}^{3} \frac{( A _{i}^{†} ) ^{n_{i}}}{n _{i} !} ∣0 ⟩ .

They have energy

ℏ ω (n_{1} + n_{2} + n_{3} + 3/2)

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