# Recent content by ala

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

For that x, I have asymptotic solution. I want to find numerical solution in the middle, but don't know how. (I don't have 1 ODE, I have system of ODE)
2. ### [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...
3. ### Proof of invariance of dp1*dp2*dp3/E

Yes, that is equivalent to p^2=m^2*c^2 (p is 4-vector of momentum). So for x, I can watch hypersurface given by equation x^2=c*\tau (x is 4-vector, and \tau proper time). So the rest is same and conclusion is worng (namely that dxdydz/t is invariant)
4. ### 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...
5. ### 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...
6. ### Problem book in atomic physics?

Is there any problem book in atomic physics?
7. ### 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...
8. ### Projection postulate - can it be verified?

Well my question was (among others) about possibility that measurement changes eigenvalue of continuous spectra significantly. (because from Landau's derivation and don't see why should fi_n be close to PSI_n)
9. ### Projection postulate - can it be verified?

I am not quite sure that I understand what you are saying. (because of notation) If fi_n and PSI_n are not same that means that measurement changed state that gives result f_n with certainty. (meaning it changed eigenstate) So you say that it is just possible for continuous spectra, but can...
10. ### Projection postulate - can it be verified?

So how do you see that for discrete spectra fi_n(x) is equal to PSI_n(x)? Well I don't see the connection between this and my question.
11. ### Projection postulate - can it be verified?

I have just realized that I should write Landau's argumentation because many of you don't have his book. 1) QM cannot be founded without classical mechanics (which is not case for relativistic and classic mechanics), because particles don't have definite path or other dynamical characteristics...
12. ### Projection postulate - can it be verified?

In this chapter authors are not using Dirac notation but they say that measuring device's spectra is generally speaking continuous (but they didn't say that it has to be). I don't see why their reasoning cannot be applied to discrete spectra. It's really odd thing that for continuous spectra...
13. ### Projection postulate - can it be verified?

I was talking about discrete spectra (but I forgot to say that), Landau is also talking about discrete spectra. It seems that Landau is wrong but it is hard to believe in that. Any other explanations?
14. ### 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...
15. ### Lie group and algebras

Yes, you are right, I forgot to say that they are finite dimensional. (In all statements where representation is used)