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    [Numerical] System of first order ordinary diff equations with given asymptotic

    I have system of first order ordinary diff equations, indipendent variable is x cordinate. I know asymptotic solution in left and right region (i.e. when x->-infinity or x->infinity, e.g. when abs(x)>1000), it's const plus exponentially falling function. I want to find numerical solution in...
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    Proof of invariance of dp1*dp2*dp3/E

    If we introduce four-dimensional coordinate sistem with component of four-momentum on axis, then dp1*dp2*dp3 can be considered as zeroth component of an element of hypersurface given by p^2=m^2*c^2. Element of this hypersurface is parallel to 4-vector of momentum so we have that dp1*dp2*dp3/E is...
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    Irreducible tensor (second or higher rank)

    When one want to find selection rules for matrix element of (for example) electric quadrupole moment tensor Qij, irreducible components of Qij are needed to apply Wigner-Eckart theorem. When symmetry group is SO(3) irreducible component can be found using what we know from addition of angular...
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    Problem book in atomic physics?

    Is there any problem book in atomic physics?
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    Gibbs distribution and Bose statistics

    For photon gas chemical potential is zero. It is because derivate of free energy with respect to number (T, V fixed) of particles is zero in equilibrium. (free energy has minimum). I was wondering why cannot I apply this reasoning to conclude (wrong) that chemical potential is zero for any Bose...
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    Projection postulate - can it be verified?

    Many books on QM state this so called von Naumann projection postulate i.e. that after the measurement system is in eigenstate of operator whose eigenvalue is measured. But in Landau Quantum Mechanics in chapter 7, author explicitly says that after the measurement system is in a state that...
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    Lie group and algebras

    Here is few statements that I proved but I suspect that are incorrect (but I can't find mistake), term group means Lie group same goes for algebra: 1. Noncompact group G doesn't have faithfull (ie. kernel has more that one element) unitary representation. Proof: If D(G) is faithfull unitary...
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    Problem concerning smooth manifolds

    A={ {{cos x, -sin x},{sin x, cos x}}|x \inR}, show that set A is smooth manifold in space of 2x2 real matrix. What is tangent space in unity matrix? My questions about problem: 1. What is topology here? (Because I need topology to show that this is manifold) 2. In solution they say that...
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    Problem book on manifolds

    Is there some solved problem book about manifolds? (or where can I find solved problems on manifolds)