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Find the wave function of the particle in one dimensional potential well. |
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Answer» The particle in one dimensional potential well ∴ V = 0 for 0 < x < L V = ∞ for x ≤ 0 and x ≥ L The particle present in a box so outside wave function Ψ is zero. Ψ = 0 for x ≤ 0 x ≥ L Schrodinger's equation time independent \(\frac{∂^2\psi}{∂x^2}+\frac{2m}{h^2}\) (E - V) Ψ = 0 one dimensional V = 0 \(\frac{∂^2\psi}{∂x^2}+\frac{2m}{h^2}\) (E) Ψ = 0 Let the factor 2m/h2 E = k2 then \(\frac{∂^2\psi}{∂x^2}\) + k2 Ψ = 0 ...(1) then general solution of equation (1), we get Ψ = A sin kx + B cos kx |
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