{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

c120a_lecture31_sp2007

c120a_lecture31_sp2007 - Chem 120A Spring 2007 Spin...

This preview shows pages 1–2. Sign up to view the full content.

Chem 120A Spin Statistics/Approximation Methods 04/09/07 Spring 2007 Lecture 31 Reading: Ratner Schatz Chapter 9 1 Spin our notation later on. integer or half integer. we can label our kets as b . (The letters j and m are standard notation, but a and b are not.) We will use the standard j , m notation from now on. For a given value of j , m can take on values of - j , - j + 1 , - j + 2 ... j - 2 , j - 1 , j . A few examples are shown in Figure 3 specialize the above arguments to orbital angular momentum, we would simply replace all J ’s with L ’s and all the j ’s with l ’s. For spin angular momentum, we replace all J ’s with S ’s, all the j ’s with s ’s, and all the m ’s with m s ’s as shown below. Last time we looked at the algebra of angular momentum in quantum mechanics and then specialized to spin angular momentum. Remember that every fundamental particle has a particular value of “ s ”. That value of s then determines the possible values of m s . We then gave the fundamental theorem of spin statistics: If s is an integer = 1, 2, 3, .... then the particle is a boson. Identical bosons are symmetric under pairwise exchange: ψ ( 1 , 2 ) = ψ ( 2 , 1 ) . If s is a half-integer = 1/2, 3/2, 5/2... then the particle is a fermion. Identical fermions are antisymmetric under pairwise exchange: ψ ( 1 , 2 ) = - ψ ( 2 , 1 ) . Let’s look at two identical fermions, for instance two electrons in an He atom. Electrons have s = 1 / 2, therefore m s has possible values of + 1 / 2 and - 1 / 2. The total wavefunction has a spatial part (see Lectures 20,21,24) and a spin part. Ψ ( r 1 , r 2 , s 1 , s 2 ) = ψ ( r 1 , r 2 ) φ ( s 1 , s 2 ) (1) where ψ ( r 1 , r 2 ) describes the spatial part of the two electrons and φ ( s 1 , s 2 ) describes the spin angular mo- mentum of the two electrons. Above we stated that the wavefunction describing the two particles must be antisymmetric overall. If the spatial part of the wavefuntion is symmetric, then the spin part must be antisymmetric. If the spin part is symmetric, then the spatial part must be antisymmetric (remember that the product of a symmetric and antisymmetric function is overall antisymmetric). We will use a + subscript for symmetric wavefunctions and a - subscript for antisymmetric wavefunctions.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern