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# 8: Central Potentials


In this chapter, we shall investigate the interaction of a non-relativistic particle of mass $$m$$ and energy $$E$$ with various so-called central potentials, $$V(r)$$, where $$r=(x^{\,2}+y^{\,2}+z^{\,2})^{1/2}$$ is the radial distance from the origin. It is, of course, most convenient to work in spherical coordinates—$$r$$, $$\theta$$, $$\phi$$—during such an investigation. (See Section [s8.3].) Thus, we shall be searching for stationary wavefunctions, $$\psi(r,\theta,\phi)$$, that satisfy the time-independent Schrödinger equation (see Section [sstat]) $\label{e9.1} H\,\psi = E\,\psi,$ where the Hamiltonian takes the standard non-relativistic form $\label{e9.2} H = \frac{p^{\,2}}{2\,m} + V(r).$

This page titled 8: Central Potentials is shared under a not declared license and was authored, remixed, and/or curated by Richard Fitzpatrick.

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