- #1

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- Homework Statement
- Problem e). See picture

- Relevant Equations
- See picture

I have found an answer to all of them (a-e) but I don’t know how to plot the function.

Thanks!

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- Thread starter Graham87
- Start date

In summary: Yeah, that looks right. Although if you had used the exponential form you would see that is equal to:$$\frac{2\hbar}{9}\big (\cos(2\theta) - 2\sin(2\theta)\big )$$And note that ##\theta## is a function of ##t## here.

- #1

- 62

- 16

- Homework Statement
- Problem e). See picture

- Relevant Equations
- See picture

I have found an answer to all of them (a-e) but I don’t know how to plot the function.

Thanks!

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- #2

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But in any case, are you really asking how to plot a constant as a function of time?

- #3

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Aha ! Like this?vela said:

But in any case, are you really asking how to plot a constant as a function of time?

- #4

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Also, doesn't ##2\hbar## seem awfully big for a spin-1/2 particle?

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you need to take the complex conjugate here

Remember that the ##\dagger## (hermitian conjugate) in linear algebra means transpose ##T## and complex conjugate ##*##, i.e.

a matrix ##A## when you do the hermitian conjugate, you do this ##A^\dagger =( A^*)^T##

- #6

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Aha, thanks. I get after correction ##(2/3)\hbar##.vela said:

Also, doesn't ##2\hbar## seem awfully big for a spin-1/2 particle?

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Aren't you suspicious that the expectation value of spin in the x-direction is constant in a z-direction magnetic field?Graham87 said:Aha, thanks. I get after correction ##(2/3)\hbar##.

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- #9

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Aha, true. I think I get it. Should it look like a trigonometric function?PeroK said:Aren't you suspicious that the expectation value of spin in the x-direction is constant in a z-direction magnetic field?

I will try again later.

- #10

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Not really. But I’m guessing something like sin(x)cos(y)?hutchphd said:

I will try again later.

Thanks!

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Also,the Hamiltonian drives the time evolution of the system. You should expect something to change over time in this case.Graham87 said:Aha, true. I think I get it. Should it look like a trigonometric function?

I will try again later.

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Still not correct.Graham87 said:Aha, thanks. I get after correction ##(2/3)\hbar##.

Could you show how you did that calculation so maybe we can spot another error?

- #13

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I used Euler formula to convert e, but I get something messy. Might my d-answer be wrong too (see pic at beginning) ?malawi_glenn said:Still not correct.

Could you show how you did that calculation so maybe we can spot another error?

Last edited:

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$$\frac{2\hbar}{9}\big (\cos(2\theta) - 2\sin(2\theta)\big )$$And note that ##\theta## is a function of ##t## here.

- #15

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Ah! I got the same now. Big thanks !PeroK said:

$$\frac{2\hbar}{9}\big (\cos(2\theta) - 2\sin(2\theta)\big )$$And note that ##\theta## is a function of ##t## here.

The expectation value of spin in quantum mechanics is a measure of the average spin of a particle in a particular state. It is calculated by taking the inner product of the state vector with the spin operator, and then taking the magnitude squared of the result.

The expectation value of spin is calculated by taking the inner product of the state vector with the spin operator, and then taking the magnitude squared of the result. This can be represented mathematically as ⟨S⟩ = |⟨ψ|S|ψ⟩|^2.

The expectation value of spin tells us the average spin of a particle in a particular state. It can also give us information about the orientation of the particle's spin in a given direction.

The expectation value of spin is related to the uncertainty principle in that it is one of the properties that cannot be known with absolute certainty in quantum mechanics. The uncertainty principle states that the more precisely we know the value of one property, the less precisely we can know another related property. In the case of spin, the more precisely we know the expectation value, the less precisely we can know the orientation of the particle's spin in a given direction.

Yes, the expectation value of spin can be measured experimentally using techniques such as Stern-Gerlach experiments. These experiments involve passing a beam of particles through a magnetic field, which causes the particles to separate based on their spin orientation. By measuring the separation of the particles, the expectation value of spin can be determined.

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