For the three-dimensional particle in a box system, the Hamiltonian is separable, i.e., . The total wave function of the system can be expressed as:

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For the three-dimensional particle in a box system, the Hamiltonian is separable, i.e., <br><img src='https://www.fatskills.com/images2/GradExams/D74F5726-6AB1-474F-96DD-FE6A310CFA26.png' height='25' width='240'/>. The total wave function of the system can be expressed as: