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  1. C

    Energy Level Separation

    Homework Statement Considering only orbital angular momentum, estimate the energy level separation between electron states in a magnetic field of 1 Tesla applied along the z direction. Homework Equations I am confused by how to even start this question! Isn't orbital angular momentum...
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    Eigenvalues and Normalised Eigenvectors

    to be of unit length...which these are right?
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    Eigenvalues and Normalised Eigenvectors

    Thank you very much. So what I have done is for eigenvalue h+g I have two equations hx+gy=hx+gx and gx+hy = hy+gy which gives x=y so eigenvalue h+g has eigenvector (1,1) and for eigenvalue h-g I have two equations hx+gy=hx-gx and hx+gy=hy-gy so x=-y so eigenvalue h-g has eigenvector...
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    Eigenvalues and Normalised Eigenvectors

    Homework Statement I have a matrix H= [h g g h] and I need to find the eigenvalues and normalised eigenvectors Homework Equations The Attempt at a Solution I subtracted lamda from the diagonal and then solved for the determinant equally zero. The eigenvalues I found were...
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    Finding the expectation value of the angular momentum squared for a wave function

    May I ask why you do not need to use the L^2 operator explicitly? How do you end up with your sum(an* am <En|H|Em>) term?
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    Relationship between Debye Temperature and Speed of Sound in Metals

    you first need to find the cut off frequency wd by using the linear dispersion relation. For the Debye model w is proportional to k. At the long wavelength limit k=pi/a where a is the dimension of the unit cell. Having found w you can then substitute it back into your first equation for temperature.
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    Wavefunctions for Indistinguishable and Distinguishable particles -

    Does that mean that my wavefunctions look correct? How would they differ for the two lowest energy states?
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    Wavefunctions for Indistinguishable and Distinguishable particles -

    Wavefunctions for Indistinguishable and Distinguishable particles - URGENT Homework Statement A one-dimensional potential well has a set of single-particle energy eigenstates Un(x) with energies En=E_o n^2 where n=1,2,3... Two particles are placed in the well with three possible sets of...
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    Energy levels of helium atom

    Homework Statement I have having difficulty explaining the splitting of helium atom energy levels for three different cases: 1)Coulomb interaction is ignored 2)Coulomb interaction is present but exchange interaction is neglected 3)Coulomb and exchange interactions are present The Attempt...
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    Structure factors

    Homework Statement I have the ionic compound cesium chloride and have been asked to use the equation p(k) = (sum over j) exp(-iK.r)f(k) to find the structure factor for x-ray diffraction from cesium and explain why it can take two values. It also asks how you would expect the intensities...
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    Eigenvectors of the hamiltonian

    So how would you calculate the other eigenvectors. Sorry I am still confused.
  12. C

    Eigenvectors of the hamiltonian

    Homework Statement The Hamiltonian of a system has the matrix representation H=Vo*(1-e , 0 , 0 0 , 1 , e 0 , e , 2) Write down the eigenvalues and eigenvectors of the unperturbed Hamiltonian (e=0) Homework Equations when unperturbed the Hamiltonian will...
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    Exchange interaction

    Homework Statement I was trying to work through some quantum physics questions and I was getting a bit confused. I know that for fermions the wavefunction must consist of spin and spatial parts of the fermionic wavefunction with opposite exchange symmetry (ie antisymmetric spin and symmetric...
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    Energy shift using perturbation theory

    Homework Statement I am looking at the relativistic correction to the kinetic energy for a hydrogen atom. I am told that the perturbation is usually written as H = -p^4/(8 m^3 c^2) and need to find the energy shift Homework Equations I know that from the perturbation theory the energy...
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    Double Pendulum !

    Double Pendulum URGENT! Homework Statement I am trying to solve this past paper question for my exam tomorrow: A double pendulum is constructed using a light rod and light inextensible strings. Two string pendulums hanging from ceiling 1m long. 0.1m from top they are connected by a light...
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    Past paper question about rates

    Homework Statement Water is falling gently into a large tank at 0.2m^3s^-1 and leaves through a small hole in the bottom of the tank of area 0.05m^2. What is the water velocity as it leaves? How full is the tank in the steady state? Homework Equations Well if the rate of water...
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    Current homework problem

    Thanks So R=l * rho /A where l is the length of the conductor rho is the electrical resistivity of the material A is the cross-sectional area of the conductor So V=IR I(1) = V/R(1) and I(2)=V/R(2) where I(1) is the inital current taking a ratio I(1)/I(2) = [V/R(1)]/[V/R(2)] =...
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    Current homework problem

    Homework Statement A light bulb has a straight metal wire filament of 50 micro metres diameter and 10mm long and when powered with a 5V constant voltage supply it draws 0.5A of current. What happens to the current if the filament is replaced with one of three times the diameter? Homework...
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    Bullet hitting a suspended mass

    I follow that really well. Thanks. I get that the mass gains a height of h=4.32mm When trying to draw the right angle triangle I get a bit confused. If the length of the hypotenuse is the length of the string. The angle at the top of the triangle is theta, the angle through which the mass...
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    Bullet hitting a suspended mass

    Homework Statement A mass of M=0.5kg is suspended from a fixed pivot by a thin rope of length l=120cm. The mass is struck by a bullet of mass m=10g with a speed of v=150m/s which embeds itself into the lead mass. What angle does the combined mass swing back to? The Attempt at a Solution...
  21. C

    Hydrogen gas

    So the Boltzmann factor is exp(-E/kT)=0.05 I still don't understand what you would take as the energy of the gas. It can't have a factor of kT because then the T would cancel......
  22. C

    Hydrogen gas

    Homework Statement A gas of hydrogen atoms has a fraction of atoms found in the n=2 quantum state of 0.05. What is the temperature of the gas? The Attempt at a Solution I think the gas molecules have an energy E=5/2kT (rather than E=kT ?? because diatomic gases have 5 degrees of...
  23. C

    Pressure and tyres

    Homework Statement Just a quick question: does a fully inflated tyre have the same mass as a tyre that is punctured or uninflated? Homework Equations The Attempt at a Solution The one that is fully inflated will have a greater pressure but I am not sure what this will mean in...
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    Inclined pendulum

    Homework Statement A train is travelling at 30m/s and decelerates and stops. During this process a passenger notices that a penduum is inclined by 10 degrees to the vertical. Estimate how far the train travels before coming to rest Homework Equations The Attempt at a Solution I...
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    Angular resolution of the eye

    thank you that makes much more sense now :smile:
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    Angular resolution of the eye

    We are only given the separation distance of the red lights but I think it is assumed that we know the wavelength of the light and the angular resolution of the eye. Since the angle is so small and sin(theta)=theta can it also be assumed that tan(theta)=theta? If so the vector triangle would...
  27. C

    Angular resolution of the eye

    Homework Statement Two red lights are separated by 5cm, perpendicular to your line of sight. How far away from them are you if they can just be resolved with the naked eye? Homework Equations angular resolution =sin(theta)=1.22lambda / D spatial resolution = 1.22(focal length * lambda)/D...
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    Newton's law of cooling and your body

    Homework Statement a body has temperature 27C at twelve oclock. The room temperature is constant at 16C. Two hours later the body was found to have a temperature of 24C. The temperature of a normal human body is 37C.Using Newton's law of cooling estimate the time of death. Homework...
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    Orthogonality and find coefficients

    Homework Statement I have that the general solution of a function is f(\rho,t)=\Sigmac(m)Jo(\alpha\rho\a) exp[-Dtm^2] where c(m) are constants. I need to find an expression for c(m) in terms of an integral Homework Equations Orthogonality relation given is \intdx x...
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