Quantum Mechanics; Expectation value

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Homework Help Overview

The discussion revolves around calculating the expectation value of energy in a quantum mechanics context, specifically at time t=0 for a given state. Participants express uncertainty about the process and the relevant concepts involved.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the multiplication of coefficients and the need for understanding the energies of the states involved. Questions arise about the relationship between eigenvalues and the expectation value, as well as the correct method to compute the expectation value using the bra-ket notation.

Discussion Status

There is an ongoing exploration of the concepts, with some participants providing guidance on the necessity of knowing the energies associated with the states and how to approach the expectation value calculation. Multiple interpretations of the problem are being considered, and participants are clarifying their understanding of the relevant equations.

Contextual Notes

Participants note the lack of complete information in the original question, which affects the clarity of the discussion. There is also mention of the need for relevant context to avoid guesswork in understanding the problem.

Stephen_G
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Homework Statement


At t=0, the system is in the state
gif.latex?%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%5Cbinom%7B1%7D%7Bi%7D.gif
. What is the expectation value of the energy at t=0?

I'm not sure if this is straight forward scalar multiplication, surprised if it was, but we didn't cover this in class really, just glossed through it. If someone could walk me through this, it would be most appreciated.

Homework Equations

The Attempt at a Solution


I just multiplied the 1/sqrt2 by 1 and i. I'm certain that this is not the correct.
 
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Stephen_G said:
I just multiplied the 1/sqrt2 by 1 and i.
How, and why?

You need to know the energies of the two states, at least as variables.

If you measure which state the particle is in, what are the possible results? What is the energy associated with each result? What is the probability?
 
Would the energies be the eigenvalues? I got those in the first portion of that question.

The first question asked for the eigenvlaues and vectors for the hamiltonian:
26i%5Csqrt5%20%26%20%5C%5C%20-i%5Csqrt5%20%26-2%20%26%20%5C%5C%20%26%20%26%20%5Cend%7Bpmatrix%7D.gif
 
Please post the full question with all relevant context, otherwise there is too much guesswork involved.

In general, how do you find the expectation value of an operator?
 
Sorry about that, I will in the future.
But, for the your question, you would just insert your expectation value into your braket <Ψ|A|Ψ> and solve, correct?
 
That works, sure.
 

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