The Three-Dimensional, Many-Particle Schrodinger Equation

4 The Three-Dimensional, Many-Particle Schrodinger Equation 

Up to now we have restricted ourselves to one-dimensional, one-particle systems. The operator formalism developed in the last section allows us to extend our work to three-dimensional, many-particle systems. The time-dependent Schrbdinger equation for the time development of the state function is postulated to have the form of Eq. (1.13)  

The time-independent Schrodinger equation for the energy eigenfunctions and eigenvalues is 

For a one-particle, three-dimensional system, the classical-mechanical Hamiltonian is 

Introducing the quantum-mechanical operators [Eq. (3.24)], we have for the Hamiltonian operator 

Ihe operator in parentheses in (3.45) is called the Laplacian operator (read as del squared )  

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