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I don't get bra-ket notation

Anonymous Fri 21 Jan 19:32:33 2022 No.14132743 View Reply Original Report

Quoted By: >>14132830 >>14133132 >>14133255

When does the product between a bra and a ket use the integral formula and when does it not?

|u>=2-i

<u|=2+i

<u|u>=(2-i)(2+i)

or

<u|u>=integral (2-i)(2+i)dx ?

Anonymous

Anonymous Fri 21 Jan 2022 19:48:54 No.14132830 Report

Quoted By: >>14132889

>>14132743
A bra of the form <u| is not a complex number. It's a functional that maps a ket to a complex number.

Anonymous

Anonymous Fri 21 Jan 2022 20:04:07 No.14132889 Report

Quoted By:

>>14132830
this. the bra is a dual vector. it maps a vector (a ket) to a scalar.

for countable vectorspaces it is possible to specify a dual vector with a vector, so making the distinction doesn't seem that profitable. for instance, given a vector $|f \rangle$ , in a 1D countable space you can make a dual vector
$\langle f | = \langle f, \ldots \rangle = \int f [/ldots] dx$

but for functional analysis on uncountable spaces you really need to keep vectors and dual vectors separate in your head. it's easy to spot these situations because the relation above will tell you your dual vectors aren't normalizable

Anonymous

Anonymous Fri 21 Jan 2022 21:12:11 No.14133132 Report

Quoted By: >>14133149

>>14132743
When you choose a basis and include a completeness relation to turn <u|u> into integral_-inf^inf dx <u|x><x|u> with the completeness relation integral_-inf^inf dx |x><x| = 1

Anonymous

View Same Google iqdb SauceNAO Ch3QM.pdf, 397KiB, 1x1

Anonymous Fri 21 Jan 2022 21:16:27 No.14133149 Report

Quoted By:

>>14133132
Bottom of page 8 if you want further reading

Anonymous

Anonymous Fri 21 Jan 2022 21:52:51 No.14133255 Report

Quoted By: >>14133481 >>14133612

>>14132743
What are good books to learn the very basics of Quantum Mechanics? I've completed my QM course but only because the prof let me pass, otherwise I would have failed. Now I decided that I will invest the effort to actually learn it, because I honestly feel ashamed. I think the course was based on J. J. Sakurai's Modern Quantum Mechanics, but I feel like a brainlet when I try to learn from that book.

Anonymous

Anonymous Fri 21 Jan 2022 22:55:35 No.14133481 Report

Quoted By:

>>14133255
sakurai makes everyone feel like a brainlet, but that's the brainletism leaving you. you read this shit over and over again before it makes sense, and even then it takes time (and sleep)

Anonymous

Anonymous Fri 21 Jan 2022 23:48:35 No.14133612 Report

Quoted By:

>>14133255
Griffiths' QM book is good. I don't know if there is really a simpler one, and honestly most of what is treated in Sakurai is also treated in Griffiths.

Some people strangely claim Griffiths is not good. I think probably they had it as a required textbook in a first class, and they did not understand things very well yet so they blame it on the textbook when really it was the best possible textbook they could have gotten.

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