Day 381: Number States |n⟩ — The Fock Space

Learning Objectives

• •Prove the existence of a ground state |0⟩ from the ladder operator algebra
• •Construct all number states |n⟩ using the creation operator
• •Derive the energy spectrum $E_n = \hbar\omega(n + \frac{1}{2})$
• •Prove the ladder operator actions: $\hat{a}|n\rangle = \sqrt{n}|n-1\rangle$
• •Understand zero-point energy as a quantum mechanical necessity
• •Build Fock states computationally and verify orthonormality

Today's Schedule (7 hours)