Radial wave function in H atom

[facenian]

helo can someone tell me where I can find detailed explanation about normalization and orthogonal properties of the radial functions since the books I've been reading do not explain enough, I thought Laguerre associated polynomials resolved the problem directly but this is not the case, the weighting function do not come up correctly and the integration variable are different in the two polynomials appearing in the integral,

 

[tom.stoer]

strange; any textbook on quantum mechanics should explain this correctly

 

[facenian]

strange; any textbook on quantum mechanics should explain this correctly

For intance, Griffiths sends you for details to L. Schiff, Quantum Mechanics(1968) a book no longer evailable in Amazon.
The problems are: 1) Normalization constant. Normalization of Laguerrre associated polynomials do not apply directly to this case and 2) Orthogonalization. We Know that \int R_{nl}(r)R_{ml}(r)r^2 dr=0,\,\,n\neq m however othogonalization of Laguerre polynomials do not apply directly either

 

[dextercioby]

Try Pauling and Wilson from 1935 by Dover and possibly reprinted since then. Also Bethe and Salpeter (1957), if available. They give all the details for your questions.

 

[phyzguy]

I think the normalization given on the Wikipedia page below is correct. Also, attached is a Mathematica notebook which verifies this normalization for n=1,2,3.

http://en.wikipedia.org/wiki/Hydrogen_atom

 

[facenian]

Try Pauling and Wilson from 1935 by Dover and possibly reprinted since then. Also Bethe and Salpeter (1957), if available. They give all the details for your questions.

ok, thanks. I bought Bethe's form Amazon at a good price.

I think the normalization given on the Wikipedia page below is correct. Also, attached is a Mathematica notebook which verifies this normalization for n=1,2,3.

http://en.wikipedia.org/wiki/Hydrogen_atom

My problem is that I want to actually calculate the normalization constant and also I want to know why they are orthonormal and as I said before Laguerre polynomial's theory do not answer this

 

[jtbell]

Try looking for a math textbook that deals with the so-called "special functions": Bessel, Legendre, Laguerre, hypergeometric, etc. I used such a textbook in an "Intermediate Differential Equations" course in graduate school about thirty years ago. Unfortunately, I don't remember the book's title or author.

 

[phyzguy]

Note that the generalized Laguerre polynomials themselves are not orthonormal unless you apply the weighting function r^n*e^-r, which is included in the H wave function. You might try this reference:

http://mathworld.wolfram.com/OrthogonalPolynomials.html

 

[jewbinson]

Try looking for a math textbook that deals with the so-called "special functions": Bessel, Legendre, Laguerre, hypergeometric, etc. I used such a textbook in an "Intermediate Differential Equations" course in graduate school about thirty years ago. Unfortunately, I don't remember the book's title or author.

"Mathematical methods for physics and engineering" has a chapter dedicated to these functions. I would also recommend this book as the essential maths reference book to anyone taking a degree in a related area (maths, physics, engineering etc).

Edit: make sure you get the latest edition (if you're going to buy it) of course