Timeline for Physical interpretation of the bra-ket notation
Current License: CC BY-SA 4.0
8 events
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| Jul 6, 2023 at 18:28 | comment | added | SvenForkbeard | Exactly. You could of course normalize $|\psi\rangle$ a priori in which case you don't need the denominator.. | |
| Jul 6, 2023 at 15:17 | comment | added | Rasmus Andersen | Thank you. Sakurai explains this concept really well also. I was just confused about the expectation value given as $E_A(\psi)=\langle\psi|A|\psi\rangle/\langle\psi|\psi\rangle$, but maybe the point is to normalize the expectation value? | |
| Jul 5, 2023 at 22:10 | history | edited | SvenForkbeard | CC BY-SA 4.0 |
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| Jul 5, 2023 at 21:56 | history | edited | SvenForkbeard | CC BY-SA 4.0 |
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| Jul 5, 2023 at 21:54 | comment | added | SvenForkbeard | It's not really coupling these two concepts together. Linear algebra is the language of quantum mechanics. It seems that you might want a good course in linear algebra (at the level of Lang say). No. $\langle \psi | A | \psi \rangle$ is the object $\langle \psi, A \psi \rangle$ which obviously depends on $A$. This is what is meant by the expectation value of $A$. On the other hand, $\langle \psi | \psi \rangle$ has no $A$-dependence, indeed taking $\psi$ to be normalized by definition means $\langle \psi | \psi \rangle = 1$ trivially. | |
| Jul 5, 2023 at 21:40 | comment | added | Rasmus Andersen | Thank you. I think it is a great idea to couple these quantum mechanical concepts to concepts from linear algebra. I do have one question. Is it correctly understood that the expectation value of an observable, say $A$, can be written as either $\langle\psi|A|\psi\rangle$ or $\langle\psi|\psi\rangle$ | |
| Jul 5, 2023 at 21:11 | history | edited | SvenForkbeard | CC BY-SA 4.0 |
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| Jul 5, 2023 at 21:06 | history | answered | SvenForkbeard | CC BY-SA 4.0 |