Why do ket vectors not have magnitudes?

  • #1
entropy1
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Why does the magnitude of a ket vector not matter?

The motivation appears to be that a state vector only can decribe a particle, or no particle.

But why shouldn't the magnitude of ket vectors not be used to represent the density of the particles, the average number of particles?

I'm am fairly new on the mathematics, in fact just starting again. ;)
 

Answers and Replies

  • #2
atyy
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The ket is the state of the entire system - so it always represents all particles.

The state of the system is a ray in Hilbert space, so kets of different magnitudes represent the same state. The most usual convention is to take all kets to be unit vectors, basically so that the probabilities sum to one.
 
  • #3
entropy1
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Thank you for your reply! :smile: I'm glad you understand my question. I'm not sure if I understand your answer, but I will dive into it! Thanks!

Oh, a question though: what do you mean with 'a ray'? :smile: Thanks again!
 
  • #4
atyy
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Oh, a question though: what do you mean with 'a ray'? :smile: Thanks again!
If one pictures each vector as an arrow of a certain length sticking out from the origin, then a ray is just that vector extended in both directions. It's just another way of saying that multiplying the vector by any complex number gives a different vector, but it is the same state.

http://www.theory.caltech.edu/people/preskill/ph229/notes/chap2.pdf (talks about rays)
 
  • #5
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Entropy: Have a look at Leonard Susskind's quantum mechanics lectures at http://theoreticalminimum.com/courses/quantum-mechanics/2012/winter. He doesn't assume much prior mathematical knowledge and spends a lot of time in the first few lectures explaining the linear algebra and interpretation of bra and ket vectors. I probably wouldn't have gotten past square one without his lectures.
 
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  • #6
atyy
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Entropy: Have a look at Leonard Susskind's quantum mechanics lectures at http://theoreticalminimum.com/courses/quantum-mechanics/2012/winter. He doesn't assume much prior mathematical knowledge and spends a lot of time in the first few lectures explaining the linear algebra and interpretation of bra and ket vectors. I probably wouldn't have gotten past square one without his lectures.
What is the plural of "apparatus"? :smile: http://theoreticalminimum.com/courses/quantum-mechanics/2012/winter/lecture-2
 

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