Recent content by jstrunk

I'm sorry but I don't understand any of that. I am doing self study, but the level I am at is like that of someone in the first few weeks of their first undergraduate QM course. At this point, the most important thing I need to understand is this: When solving Time Independent Schrodinger...

I don't understand this statement about potential energy V(x) from Griffiths Intro to Quantum Mechanics, 3rd Ed. Problem 2.1c: If V(x) is an even function (that is V(-x)=V(x)) then psi(x) can always be taken to be either even or odd. psi(x) refers to a solution of the Time Independent...

vanhees71 stated: I thought Griffiths mentioned this somewhere. See, for example, the footnote on page 97 (2nd Edition) relating to equation 3.19. "I threw away the boundary term for the usual reason", he says. I am using the 3rd Edition and I am only on page 18. So far, he hasn't given any...

Summary:: The problem solutions contain a lot of unjustified steps, making them pointless. I am trying to use Griffiths Introduction to Quantum Mechanics. He states that the wave function ##\psi## approaches 0 as x approaches infinity to make normalization work. I can accept that. But then I...

Here is what the book says about c. Let 1<c<q be minimal in ##Z^{*}_{q}## with o(c)=p. Observe that since o(c)=p we have ##c^p=1 \in Z^{*}_{q}## and it follows that ##c^k=c^{kmodp} \in Z^{*}_{q}##. The formula doesn't even make sense in the second term, which doesn't involve c. I am asked to...

My book gives this formula for the semidirect product for groups ##Z_p## and ## Z_q## for primes p<q and p divides (q-1). ##(a,b)*(x,y)=(a+_q c^bx,b+_py)## There is also an explanation of what c is but very little else. It doesn't even explain what operation adjacency represents, eq...

OK, thank you. I had it in my head that the conjugacy classes could be all different sizes and I had to look for clues work out the size of each one individually. You said that x=e is the exception. Wouldn't it be better to say that any element of Z(G) is the exception, since if x is an...

Orbit-Stabilizer Theorem: For an action of group G on set S |orb(s)|=[G:stab(s)]=|G|/|stab(s)| for any s element of S. For the action of conjugation, this becomes |cls(s)|=[G:CG(s)]|G|/|cls(s)|, CG(s) being the centralizer of s in G. Equivalence relations divide a group into orbits of...

The book I am using has a number of exercises like this: If G is a p-group, show that G cannot have exactly p+1 conjugacy classes. If G is a p-group with p+2 conjugacy classes, show that the order of G is 4. I can never solve any problem that involves connecting the number of conjugacy...

Thanks. I'll take a look but that seems to be way beyond the level that the book I am using develops this material.

Is there anywhere online where a lot of groups are listed along with their unique decomposition according to the Fundamental Theorem of Abelian Groups? Maybe if I had something like that I could reverse engineer it to figure out how they derived the decompositions. I have seen some places where...

These suggestions are not really what I am looking for. What I need is to take several specific non-isomorphic abelian groups of the same order, and show how to get their different decompositions based on the different structures of each group.

According to the book I am using, one can decompose a finite abelian group uniquely as a direct sum of cyclic groups with prime power orders. Uniquely meaning that the structures in the group somehow force you to one particular decomposition for any given group. Unfortunately, the book gives no...

I am very confused about how to find all the automorphisms of a group. The book I am using is very vague and the exercises don't show any solutions. I get how to do it for cyclic groups but not the general case. I will outline what I know of the procedure and insert my questions into it. To...

I am trying to learn group theory on my own from Schaum's Outline of Group Theory. I chose this book because there are a lot of exercises with solutions, but I have several problems with it. 1) In many cases the author just makes some handwavey statement and I have to spend hours or days trying...