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Principles of Quantum Mechanics by Dr Singh Tyagi

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Chapter 10

Three-dimensional Systems

10.1  INTRODUCTION

In Chapter 5, we discussed time-independent Schrodinger equation for a particle in various one-dimensional potentials. In this chapter, we shall discuss the structure of the Schrodinger equation and solve it for a particle moving in a (time-independent) three-dimensional potential V(r) for which the technique of separation of variables may be used. In such cases, the original three-dimensional problem reduces to simpler (one-dimensional) problems. We shall start our discussion with the study of a free particle in three-dimensional space. Then we shall discuss motion of a particle in spherically symmetric potentials V(r) (which depend only upon the magnitude r = |r|), like attractive Coulomb ...

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