Confind electron Total energy (Quantum)

[MSK]

Homework Statement

An electron in a very thin wire of length L= 1 nm (10-9 m) can be modeled as a particle in an infinite box.
Solve for total energy using boundary conditions at L

2. The attempt at a solution
WaveFunction -- > PSI = A Sin ( kx ) ;
k = n*pi/L ; A = sqrt(2/L) "After normalizing"
Boundary condition at L -- > PSI(L) = 0
now can I solve for E using this equation ?
n*pi/L = k = sqrt( 2m*E/h^2)
?

 

[Simon Bridge]

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if in doubt, solve the Schrödinger equation.