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JPMPhysics
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u and v are vector or whatever in that base, and A is an operator. What does <u|A|v> mean?
Which QM textbook are you using?JPMPhysics said:u and v are vector or whatever in that base, and A is an operator. What does <u|A|v> mean?
JPMPhysics said:u and v are vector or whatever in that base, and A is an operator. What does <u|A|v> mean?
bhobba said:It means <u|A|v> = (<u|A)|v> = <u(|A|v>) = <v|A|u> - the last is true because A is Hermitian.
For so called pure states, its an axiom of QM, called the Born rule, that the expected value of the obsevable A, E(A) is <u|A|v>. In fact its a special case of the full Born Rule E(A) = Trace (PA) where P is any state, not just a pure one.
If the above doesn't make much sense, then, as Strangerep says, we need to know exactly the textbook you are using so the answer can be pitched at whatever background it provides. What I said above is at the level of Ballentine - Quantum Mechanics - A Modern Development, which is a more advanced graduate level text. Beginning textbooks may, for example, not make a distinction between pure and non pure states.
Thanks
Bill
JPMPhysics said:I'm using Griffiths textbook. Don't you mean <u|(A|v>)? The | before the (?
The notation is used in quantum mechanics to represent a quantum state, where and
Unlike other notations, notation specifically represents the expectation value of the operator for the state to the state
Sure, let's say we have a quantum state that represents an electron's spin being up, and a state
The expectation value, denoted as , is calculated by taking the inner product of the state and the state
notation allows for the calculation of important quantities and probabilities in quantum mechanics, such as the expectation value and transition probabilities. It also helps to simplify and standardize the representation of quantum states and their operators.