Answer to Question #140817 in Quantum Mechanics for Max

Question

If partice is in three dimensional box then write wavefunction

Answer 1

The wavefunction is

$$\psi_{n_x,n_y,n_z}(x,y,z)=\psi_{n_x}(x)\psi_{n_y}(y)\psi_{n_z}(z),\\\space\\ \psi_{n_x,n_y,n_z}(x,y,z)=\sqrt{\frac{8}{L_xL_yL_z}}\cdot\text{sin}\frac{n_x\pi x}{L_x}\cdot\text{sin}\frac{n_y\pi y}{L_y}\cdot\text{sin}\frac{n_z\pi z}{L_z}$$