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Chemistry · Glossary

What is Ladder operators?

Definition 1.19 University Chemistry — Year 3 · Chapter 1 — Quantum Mechanics for Chemists: Model Systems

With x0=ℏ/mωx_0 = \sqrt{\hbar/m\omega}, the ladder operators are

a^=12(x^x0+ix0p^ℏ),a^†=12(x^x0−ix0p^ℏ).\hat a = \frac{1}{\sqrt2}\Big(\frac{\hat x}{x_0} + \frac{\iu x_0\hat p}{\hbar}\Big), \qquad \hat a^\dagger = \frac{1}{\sqrt2}\Big(\frac{\hat x}{x_0} - \frac{\iu x_0\hat p}{\hbar}\Big).
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