Braket notation Definition and 12 Threads

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...