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June 14, 2024, 08:49:26 am

Author Topic: quantum mechanics questions  (Read 11129 times)  Share 

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mark_alec

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Re: quantum mechanics questions
« Reply #15 on: May 18, 2010, 10:23:56 pm »
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I don't know how to prove it, but I know that you have to take as given.

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Re: quantum mechanics questions
« Reply #16 on: May 19, 2010, 01:02:28 am »
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Hmm perhaps it's because the integrand is complex at all times except when

Anyway thanks mark

QuantumJG

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Re: quantum mechanics questions
« Reply #17 on: June 03, 2010, 06:18:40 pm »
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Ok I have a quantum mechanics question and I thought here is probably the best place to ask it.

Anyway I have a proton in a 1-D infinite potential well and the wavefunction for it is:



One part of the question asked me what is the quantum number n, i.e. if:



I found n to be 2 (i.e. the proton is in it's first excited state), by shifting the second equation by to the left.

Another part of this question is to prove that this wavefunction is a solution to the time independent Shrodinger equation. Is this just another way of asking you to show the second derivative of is simply a constant times .
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Re: quantum mechanics questions
« Reply #18 on: June 03, 2010, 07:30:46 pm »
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I guess you could show by differentiation, but you might as well just solve the time-independent schrodinger equation anyway. It wouldn't be a long derivation and it's probably in your book




QuantumJG

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Re: quantum mechanics questions
« Reply #19 on: June 03, 2010, 07:43:18 pm »
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Thanks.

How is your exam timetable? Mine is pretty good quantum & special on the 9th, thermal and classical on the 11th, Real Analysis on the 17th and Introductory personal finance on the 18th.

This year I have really learnt that I love physics (definately more than maths), but I still enjoy maths. You are lucky to do PDE's next semester I have to wait until next year.
2008: Finished VCE

2009 - 2011: Bachelor of Science (Mathematical Physics)

2012 - 2014: Master of Science (Applied Mathematics/Mathematical Physics)

2016 - 2018: Master of Engineering (Civil)

Semester 1:[/b] Engineering Mechanics, Fluid Mechanics, Engineering Risk Analysis, Sustainable Infrastructure Engineering

Semester 2:[/b] Earth Processes for Engineering, Engineering Materials, Structural Theory and Design, Systems Modelling and Design

QuantumJG

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Re: quantum mechanics questions
« Reply #20 on: June 03, 2010, 09:38:08 pm »
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This is another question and I want critique with my answers.

i.)

Normalisation implies that:





(I cut out a lot of crap since the wave-functions being orthonormalised means that after a bit of tedious work you get to that line)





i.e. I found this to be the normalisation condition.

ii.)

First to see if the energy is an eigenvalue





So the energy is not an eigenvalue and hence the energy is not a sharp observable.













I'm not 100% sure if this is right.
2008: Finished VCE

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2012 - 2014: Master of Science (Applied Mathematics/Mathematical Physics)

2016 - 2018: Master of Engineering (Civil)

Semester 1:[/b] Engineering Mechanics, Fluid Mechanics, Engineering Risk Analysis, Sustainable Infrastructure Engineering

Semester 2:[/b] Earth Processes for Engineering, Engineering Materials, Structural Theory and Design, Systems Modelling and Design

full of electrons

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Re: quantum mechanics questions
« Reply #21 on: June 03, 2010, 10:51:27 pm »
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Back to the original question. Isn't the integral of a Gaussian sqrt(pi)? or something similar, I'm afraid I don't actually know, it'll be in some table of integrals.

Gee, your quantum course seems harder than mine (and i reckon mine is hard enough)

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Re: quantum mechanics questions
« Reply #22 on: June 03, 2010, 11:05:06 pm »
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QuantumJG the steps you take seem alright to me... although I wouldn't take my own advice at the moment. My quantum exam is in a while so I haven't really thought much about it recently...

My exam time-table is quite spread out,
8th June: Take-home ODEs and Vector Calc exam, worth 20%
11th June: Thermal Exam, worth 35%
21st June: Analysis Exam, worth 70% (and wow I would be stoked with anything near a 70% on the exam)
23rd June: Quantum Exam, worth 40%
« Last Edit: June 03, 2010, 11:09:06 pm by /0 »

Cthulhu

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Re: quantum mechanics questions
« Reply #23 on: June 03, 2010, 11:12:01 pm »
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wtf TAKE HOME EXAMS? Do want.

I had so much trouble with my last QM assignment. It involved Bessel Functions and Circular Infinite Wells and it made me sad :(

QuantumJG

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Re: quantum mechanics questions
« Reply #24 on: June 08, 2010, 02:32:20 pm »
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I just want my answer to this question to be criticised.

i.)

Let

Therefore looking at the LHS of the Schrödinger equation:




And now the RHS:





Constant (Call it E)



Equation to find



Equation to find

ii.)

« Last Edit: June 08, 2010, 02:35:36 pm by QuantumJG »
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Re: quantum mechanics questions
« Reply #25 on: July 24, 2011, 06:03:15 pm »
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In Zetilli it gives a completeness relation for the basis of spin 1/2 states:

If and , then



But how does this matrix multiplication make sense?

mark_alec

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Re: quantum mechanics questions
« Reply #26 on: July 24, 2011, 06:25:38 pm »
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The matrix multiplication makes sense if you treat it as a direct (or Kronecker) product.

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Re: quantum mechanics questions
« Reply #27 on: July 26, 2011, 01:16:11 am »
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Thanks mark, I didn't realise it was a direct product