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I have begun reading chapter 11 of Zwiebach's "A First Course in String Theory" 2nd edition. Section 11.2 deals with the Heisenberg and Schrodinger pictures. Both pictures will use the same "state space".

What is a state space? On pages 204 - 205 of Zwiebach's text, he mentions how to construct a state space of a simple harmonic oscillator starting from a vacuum state $| 0 \rangle$ and acting on it. I don't recall an earlier mention of state space in my reading thus far. From this, I am leaning toward thinking that state space might just be a particle accounting device. I am thinking given some position, and or momentum, the state space is the number of particles with it. I would have thought this is what Fock space was.

What is a state space in quantum mechanics?

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    $\begingroup$ Are you studying string theory without having first studied nonrelativistic QM (like particle in a box, simple harmonic oscillator, hydrogen atom, etc.)? Normally Hilbert space is introduced there. $\endgroup$
    – Ghoster
    Commented Nov 27, 2022 at 6:28
  • $\begingroup$ @Ghoster I studied non-relativistic QM in undergrad, like other physics students but I don't know if I quite grasped the concepts there. This semester I am only taking graduate classical mechanics, math methods, and graduate string theory this semester. I have 3 undergrad quantum classes but maybe I did not pay the best attention to these things back then. We did do free particle, particle in a box , simple harmonic oscillator, hydrogen atom and so forth, but I also had a bit of a long gap between undergrad and grad school $\endgroup$
    – cows
    Commented Nov 27, 2022 at 6:36
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    $\begingroup$ Hmm. In that case, after getting an answer here, I suggest reading The Principles of Quantum Mechanics by Dirac to consolidate your understanding of QM. The basic idea is that since quantum states can be superposed, they are vectors in a complex vector space. This space of quantum states is where the operators of QM act on state vectors to produce other state vectors. This is true even when there is only one particle $\endgroup$
    – Ghoster
    Commented Nov 27, 2022 at 6:55
  • $\begingroup$ @Ghoster woot I got an $A^-$ in the string class. Ok so I just asked a question on the math site, somewhat unrelated to this question but I remembered you know these kinds of things so I figure I would drop a link to the question here. math.stackexchange.com/questions/4656679/… $\endgroup$
    – cows
    Commented Mar 11, 2023 at 4:10
  • $\begingroup$ Congratulations! Unfortunately, I can’t help you with that question you posted on Math SE. Also, I doubt that you’re going to get help with it there, but we’ll see. $\endgroup$
    – Ghoster
    Commented Mar 11, 2023 at 5:21

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