I've been working through some dirac notation and I'm stuck...(adsbygoogle = window.adsbygoogle || []).push({});

Here's where I'm at:

I understand that an expectation value: <x> = ∫ ψ* x ψ dx = <ψ|xψ> = <ψ|x|ψ>

Also, we can say H|ψ> = E|ψ> where E is an eigenvalue of the operator H and |ψ> represents a state your acting on.

I get that you can represent a vector 'in Hilbert space' instead of a wavefunction inside the ket and these can be operated on to transform your vector into another vector, Q|a> = |b>

|a> represents a column vector, <a| represents a row vector

It's taking some time to get used to using Dirac notation, and I've come across this in some angular momentum notes:

Lz|m,l> = mħ|m,l> .. So Lz is the operator, mħ is the corresponding eigenvalue. But what does having two values in the ket mean?

Does, L|m,l> = L|m> + L|l>

Moreover, what if we have:

<l,m|L+L-|l,m>

Should this be written in more classical notation as ∫ (l,m)* L+L- (l,m)* dx

Any guide or text book with a good section on Dirac formalism would be great, I've been looking but can't find anything to explain this trickier stuff. I've attached a page of my notes so that it's more clear with what I'm working with. I've read through Griffith's introduction to quantum mechanics chapter on Dirac formalism but I'm still getting undone by it!

Thanks,

Leon

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# Dirac Notation!

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