O'Reilly logo

Student Solution Manual for Mathematical Methods for Physics and Engineering, Third Edition by M. P. Hobson, K. F. Riley

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

18

image

Special functions

image

18.1  Use the explicit expressions

image

to verify for  = 0, 1, 2 that

image

and so is independent of the values of θ and ϕ. This is true for any ℓ, but a general proof is more involved. This result helps to reconcile intuition with the apparently arbitrary choice of polar axis in a general quantum mechanical system.

We first note that, ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required