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Find the wave function of the particle in one dimensional potential well.

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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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