Braket notation Definition and 13 Threads

First, I need to check that I have the 3 notations correct for an inner product in finite vector spaces over a complex field; v* means: given the isomorphism V to V* then: (a) physicists and others: (u,v)=v*u ; linear in the second argument (b) some mathematicians: (u,v)=u*v; linear...

Starting with finding the probability of getting one of the states will make finding the other trivial, as the sum of their probabilities would be 1. Some confusion came because I never represented the states ##|\pm \textbf{z}\rangle## as a superposition of other states, but I guess you would...

##U_1 \otimes U_2 = (1- i H_1 \ dt) \otimes (1- i H_2 \ dt)## We can write ## | \phi_i(t) > \ = U_i(t) | \phi_i(0)>## where i can be 1 or 2 depending on the subsystem. The ## U ##'s are unitary time evolution operators. Writing as tensor product we get ## |\phi_1 \phi_2> = (1- i H_1 \ dt) |...

Is |x+y> = |x> + |y> ? Thank you.

Homework Statement In the absence of degeneracy, prove that a sufficient condition for the equation below (1), where \left|a'\right> is an eigenket of A, et al., is (2) or (3). Homework Equations \sum_{b'} \left<c'|b'\right>\left<b'|a'\right>\left<a'|b'\right>\left<b'|c'\right> = \sum_{b',b''}...

Homework Statement In Sakurai's Modern Physics, the author says, "... consider an outer product acting on a ket: (1.2.32). Because of the associative axiom, we can regard this equally well as as (1.2.33), where \left<\alpha|\gamma\right> is just a number. Thus the outer product acting on a ket...

This might be trivial for some people but this has been bothering lately. If P is momentum operator and p its eigenvalue then the eigenfunction is up(x) = exp(ipx/h). where h is the reduced Planck constant (sorry can't find a way to make the proper notation). While it can also be proved that...

If x,y,z are the position operators. Is it true that: <φ|x|φ> + <φ|y|φ> + <φ|z|φ> = <φ | x+y+z| φ> ? So that if, for example, one wanted to compute <φ|r|φ> (where r =x+y+z), then they would just have to sum the parts. I know that for scalars, a and b, we have the following...

To me, braket notation just seems much easier and more intuitive than the approach from Griffiths. And yes, I learned QM through a text that used braket notation.

I'm a complete noob with Braket and I've only just started getting to grips with it. For completeness' sake though (from the book I'm currently reading), I can't seem to find a definition for: \langle J_z \rangle Would this just be the "magnitude" of J_z? Thanks

Ok, here is my question. When you have < r | i >, this equals Sri. So logically if that is that case, if you had SriSaj this would equal < r | j >< a | j >, right? If so, then what does < r | j ><a | j > equal? I'm working a problem where I am trying to get a final answer of < r | h | a...

How do you work out the commutator of two operators, A and B, which have been written in bra - ket notation? alpha = a beta = b A = 2|a><a| + |a><b| + 3|b><a| B = |a><a| + 3|a><b| + 5|b><a| - 2|b><b| The answer is a 4x4 matrix according to my lecturer... Any help much appreciated...

the question: Let {|u>,|v>} be a basis for a linear space, suppose that <u|v>=0, then prove that: A|v>=<A>I|v>+\delta A|u> where, A is hermitian operator, and <A>=<v|A|v>,\delta A= A-<A>I where I is the identity operator. my attempt at solution: basically, from the definitions i need...