Partial differential equations

This chapter focuses on partial differential equations, which are equations that contains partial derivatives. It shows different examples that demonstrate a number of important principles in the solution of partial differential equations. The chapter describes the general solutions as well as the method of separation of variables. It particularly looks at the time-independent Schrödinger equation for the particle in a rectangular box, and in a circular box, and for the hydrogen atom. Furthermore, it discusses how the one-dimensional wave equation is applied to the vibrations of an elastic string, such as a guitar string. The chapter also introduces the phenomenon of degeneracy.

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