Schrodinger wave equation and operators
Quantum Chemistry (UG) · Chemistry
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Interactive 3DA travelling wave ribbon. Raise the amplitude to make it taller, the frequency to make it faster.
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Study notes
For a particle trapped between x=0 and x=L, the allowed ψ are ψₙ = √(2/L)·sin(nπx/L). Find the energies. Step 1: Apply kinetic energy operator: -(ℏ²/2m)(d²/dx²) to ψₙ. Step 2: Second derivative of sin(nπx/L) gives -(nπ/L)²·sin(nπx/L). Step 3: So Ĥψₙ = (ℏ²n²π²/2mL²)·ψₙ. Step 4: Eigenvalue Eₙ = n²h²/8mL² — energy is quantised, n = 1, 2, 3…