Taking first semester Quantum Mechanics and our first assignment is some pretty basic stuff related to the braket notation.
I'm realizing I was never very fluent in my complex conjugates and how to deal with absolute values (yikes!).
I'm wondering if there are some good examples anywhere online regarding normalization of a wave state? Or even somewhere I can check my work to make sure I'm correct.
[math]1= C^* ( 3\langle+| + e^{i\pi/3} \langle-|)C(3\langle+| - e^{i\pi/3} \langle-|)[/math] And in previous problems I end up with |C|^2= -1/7, which doesn't make sense.
Bras and kets are complex conjugates of each other, so just take the complex conjugate of the ket then slam them together and solve.
Lucas Clark
I know. But what am I doing wrong here? How can the absolute value of C^2 be negative??
Ayden Hughes
Your bra has picked up a minus on the 4, but 4 isn't complex. [eqn] | \psi \rangle = 3 | + \rangle + 4 | - \rangle \\ \implies \langle \psi | = 3 \langle + | + 4 \langle - | [/eqn]
Isaac Morales
But I thought the bra was the conjugate? Hmm, something I'm not getting here. I mean it makes sense, so you only switch the signs if the 'b' term in the complex number is imaginary?
What about this, pic realted.
Brandon Mitchell
When you take the complex conjugate of something the sign attached to the [math] i [/math] changes, so [eqn] \left ( e^{ i \pi / 3 } \right ) ^{*} = e ^ { -i \pi / 3 } [/eqn]
Fuck, apologies for the sideways shit. Didn't appear that way on my device.
Thanks!
Much thanks! My complex conjugation skills are questionable. Never formally learned it or practiced it. I know how to deal with i, but not conjugation and such. So thanks.
Andrew Davis
Yes, that's it.
Connor Bennett
What do [math]| - \rangle[/math] and [math]\mid + \rangle[/math] denote?
My understanding is that brakets just denote the standard hermitian scalar product, no?
Gavin Thomas
Awesome.
Lastly it is asking me to find the probabilities of finding spin up or spin down along all THREE cartesian axes. Use braket notation for the whole thing.
I don't see what differences would be between the axes? I can do the calculation for the z-axis, but what would the difference be for the x/y axes?
Christian Sanders
Bra-ket notation is such cancer.
Dominic Brooks
In this context, it's the spin state of a particle.
Bentley Ortiz
Bumping this.
Carter Clark
Consider the complex conjugate to just mean that i becomes (-i)
Carson Harris
brilliant!
Oliver Ortiz
why would this be brilliant? its the definition of complex conjugate.
Hudson James
Because I never viewed it that way. Only the dumb a+\-bi form.