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    I How do i find the eigenvalues of this tough Hamiltonian?

    I have this Hamiltonian --> ( Where each G is a matrix. I want to find the eigenvalues but I'm getting hung up on the fact that there are 6 indices. Each G matrix lives in a different space so I can't just multiply the G matrices together. If I built this Hamiltonain...
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    How do I find the energies of these states?

    1. Homework Statement Here is the problem: 2. Homework Equations |psi_s_ms> = |s, ms> ⊗ Σ D_i_j |psi_i, psi_j> 3. The Attempt at a Solution I know the singlet state in the |s, ms> basis is |0,0> = (1/sqrt(2))[ |up, down> - |down, up>] and that the hamiltonian for...
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    Find probability of spin state after certain time.

    1. Homework Statement Question: (only part c) 2. Homework Equations From part a) I got |psi> = (1/sqrt(2))(e^(iwt/2)|z-up> + ie^(-iwt/2)|z-down> I expanded this wave function in the x-spin basis and got, |psi> = (1/(2))[(e^(iwt/2)+ie^(-iwt/2))|x-up> +...
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    What's the difference between these two equations?

    say we have some wavefunction |psi> and we want to find the probability of this wavefunction being in the state |q>. I get that the probability is given by P = |<q|psi>|^2 since we're projecting the wavefunction onto the basis state |q> then squaring it to give the probability density. However...
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    Do ladder operators give integer multiples of ћ?

    "Any number such that a given matrix minus that number times the identity matrix has a zero determinant." I don't see how this answers the question. should non-integer multiples of ћ be omitted or not?
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    Do ladder operators give integer multiples of ћ?

    Say I apply a raising operator to the spin state |2,-1>, then by using the the equation S+|s,ms> = ћ*sqrt(s(s+1) - ms(ms+1))|s,ms+1> I get, S+|2,-1> = sqrt(6)ћ|2,0> Does this correspond to a physical eigenvalue or should I disregard it and only take states with integer multiples of ћ as...
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    How is this equation for <x|P|x'> derived?

    but the 3rd line has <x'|x> not <x|x'>. Am I missing something?
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    How is this equation for <x|P|x'> derived?

    Thanks for replying. The 2nd line to the 3rd line is where I get lost.
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    How is this equation for <x|P|x'> derived?

    Thanks for the reply! but the whole reason we need to figure out < x | Px | x' > in the first place is because the identity operator is inserted. What's the point? Also how to do you do this derivation step by step? I'm very confused I think my prof. is skipping steps :
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    How is this equation for <x|P|x'> derived?

    Image: How is the boxed equation arrived at when looking at the step before? I think I need clarification on a few key ideas: in words, does < x | p | ψ > mean, "The momentum operator acting on the state vector, then projected onto the position basis"? If so, wouldn't...
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    Exponentials or trig functions for finite square well?

    How do you know when to use exponentials and trig functions when solving for the wave function in a finite square well? I know you can do both, but is there some way to tell before hand which method will make the problem easier? Does it have something to do with parity?
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    How do I plot this probability density over time?

    How can you tell if a given wave function isn't an eigenstate of the hamiltonian? I just don't get how if |Ψn(x, y)|^2 = |Anψn(x)e^-iEnt/h-bar|^22 and Ψ is a pure state, how doesn't the exponential factor cancel out in 1 = ∫ |Ψn(x, y)|2 dx ?
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    How do I plot this probability density over time?

    Here's the question: I normalized the wave function and got A = sqrt(315/8L^9) but how would I plot representative snapshots if the exponential factor will cancel when I square it? It's not a mixed state so it shouldn't depend on time as far as I can tell. Should I use...
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    How do I solve these coupled Differential Equation?

    1. Homework Statement dNa/dt = -Na/Ta where Na is the function and Ta is the constant dNb/dt = Na/Ta - Nb/Tb where Nb is the function and Tb is the constant 2. Homework Equations My Prof said Nb(t) has the form Nb(t) = Cexp(-t/Ta) + Dexp(-t/Tb) 3. The Attempt at a Solution I know the first...
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    Should I repeat second year?

    This is the part I'm most frustrated about. I only really started working my ass off near the end so I could pass. I'm pretty much up to speed with what I need to know (and in some cases ahead of other students) only through self studying. I know what I should know for a 3rd year physics...
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    Should I repeat second year?

    Yes my school will replace grades. I learned so much about time management towards the end of the year. I know if I retook 2nd year I would do a lot better, but there's no making up for first year.
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    Should I repeat second year?

    So I got killed this past year in physics. Combined with the fact that I slacked off a lot in first year, I have an awful GPA. It's currently sitting at 1.66 ( out of 4.3) I need ~2.0 to get into honors physics. I'm guessing the possibility of grad school is out the window. I've been studying...
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    I Need Some Academic Guidance

    I just finished second year physics and I passed everything but not by a lot. My cum GPA is ~1.7 and program GPA is ~1.8. I've done the math and I would need at least a A+ on every single course for the next 2 years to get my GPA up to only a 3. First year didn't treat me too well and and 2nd...
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    How do I solve this differential Equation

    Thanks for the replies, it was just a simple separation of variables problem. It's strange how you sometimes forget the basics as your knowledge grows.
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    How do I solve this differential Equation

    1. Homework Statement y3(dy/dx) = (y4 + 1)cosx 2. The attempt at a solution I solved for the homogeneous equation which is y = Ce-sinx Where C is some constant for the particular solution I tried Asinx + Bcosx where A and B are constants but when subbing in it's gets very messy. How...
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    MATLAB [MATLAB] Modeling response of a particle in an anharmonic potential

    Thank you I'll try it. I'm wondering if it would be more beneficial/ shed more light if I plotted x as a function of time. In that case I solved lagrange L = K - U = .5mv^2 - x^2 - x^3 since U = x^2 + x^3 the associated equation of motion is then ma = -3x^2 - 2x I would then need to solve...
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    MATLAB [MATLAB] Modeling response of a particle in an anharmonic potential

    Yes my goal is to plot a potential vs. displacement curve. Is this even possible considering the number of functions in the first equation above? Here's some of my code: For simplicity, I assume period T(E) = 1 %Define Functions %For a,b = 1 %U = ax^2 + bx^3 %Assuming T(E) = 1 U = @(x)...
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    MATLAB [MATLAB] Modeling response of a particle in an anharmonic potential

    I'm trying to model the response of a particle in an anharmonic potential in MATLAB. I know that writing position, x as a function of potential energy U is, where T is the period, m is mass, and E is the energy of the system. How would I get a function for T(E) since it's not independent of...
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    Why does infinite potential well give rise to standing wave?

    For a particle in a box that is described with a wave function, why can there only be a standing wave when there is an infinite potential well? From my understanding, the infinite potential well makes it impossible for the particle to tunnel through the barrier and so the wave function cannot...
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    Programs Should I do a minor with a physics major or specialize in just physics

    I have to decide whether to major in physics and minor in something else or to do a specialization degree in physics for undergrad. Now a specialization degree (SSP) is basically a major degree on steroids; it's a major honours degree with some graduate courses stacked on top of it so that more...
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    Programs What degree should I get for working in quantum technology?

    I'm a second year physics major and I want to work in quantum engineering. I think it's the future of technology. What degree should I do? I'm pretty much torn between physics and engineering physics. Obviously there's a trade off: engineering physics focuses more on applying concepts to the...
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    Studying pure physics or astrophysics for cosmology graduate study

    Hi there, I need to choose my major in a week and it's between physics or astrophysics. Most of the courses are the same except a few: The different courses: Physics: statistical mechanics, solid state physics, and nuclear and particle physics Astrophysics: Intro to astro...
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    Am I missing out by being and electrical engineer?

    My goal and dream since I was 16 was to study engineering physics at a certain university. I just loved the idea of combining physics (both theoretical and experimental) with the practicality and applications that come with being an engineer. However, due to various factors which I won't get...
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    Admissions Applying to engineering science

    I would like to apply to engineering science at the University of Toronto and I was wondering if had a chance of getting in. I'm going into grade 12 next year and my marks were not very good this year due to some circumstances.In grade 11 my average was 85% which was low because I was taking...
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    Engineering Science at U of T

    Hi everybody, I was wondering if I could get into engsci at U of T. I'm currently going into grade 12 and I feel as if I'm at a disadvantage. My school is extra hard which makes my marks lower than the average student at a regular school. I've already taken grade 12 advanced functions and...