Question

The wave function of a particle in a box is given by ----
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Answer 1

Answer:

The wavefunction for a quantum-mechanical particle in a box whose walls have arbitrary shape is given by the Helmholtz equation subject to the boundary condition that the wavefunction vanishes at the walls.

Answer 2

Helmholtz equation

The Helmholtz equation is the straight differential equation. Where is the Laplacian, is the sufficiency, and is the wavenumber. The Helmholtz condition is additionally an eigenvalue condition. The Helmholtz differential equation can be tackled by the detachment of factors in just 11 direction frameworks. The Helmholtz condition frequently emerges in the investigation of actual issues, including halfway differential conditions (PDEs) in both existences. The Helmholtz equation, which addresses a period-free type of the wave condition, comes about because of applying the procedure of detachment of factors to decrease the intricacy of the investigation.