Hi, Did you noticed that in master qapply(Jx*JxKet(...)) does not evaluate to ...*hbar*JxKet. Jz*JzKet evaluates as expected but not the other two base kets. Maybe it has nothing to do with your problem, but as you are rewriting operators and states it may intervene.
Also concerning the printing see below. Stefan On 16 June 2011 09:04, Sean Vig <[email protected]> wrote: > Hi all, > > In working on some stuff with spin states, I ran into some problems with > the current implementation of the Wigner small-d matrix, Rotation.d in > sympy.physics.quantum.spin. I had written methods to change bases using the > Wigner D-function [0] and in testing decided to try > >>>qapply(JzBra(1,1)*JzKet(1,1).rewrite('Jx')) > which should be 1, as the spin ket is rewritten in the Jx basis and then > back to the Jz basis to apply the innerproduct, but I have that it gives 0. > I traced this back to a bug in the Rotation.d function, which currently has > an open issue [1]. For the Wigner D-function and the small d-matrix, the > conventions laid out in Varshalovich "Quantum Theory of Angular Momentum". > It seems the d-matrix is fine for positive values of angle argument, but > does not obey the symmetry d(j,m,mp,-beta)=(-1)**(m-mp)*d(j,m,mp,beta) and > does not agree with the tables in Varshalovich. Those terms that fail for > the j=1 case are in an XFAIL test in my branch. What is odd is that when I > ran the equation used to define the d-matrix through Mathematica, I got > results that agreed with the sympy output, so the problem may be in the > equation and not a bug in the code. If anyone could take a look at that, I'd > appreciate it. > > The function in question is the Rotation.D function, which is invoked as: > >>>Rotation.D(j, m, mp, alpha, beta, gamma) > where alpha, beta, gamma are the Euler angles of the rotation, expressed as > a passive transformation, and j,m,mp satisfy: <j,m|R(alpha,beta,gamma)|j,mp> > for the rotation operator R. The D-function invokes the small d-function, > which is done as: > >>>Rotation.d(j, m, mp, beta) > > > Another thing is even if the right values were given, my methods would not > give the right results. Comparing to [2], when I rewrite a Jx ket in the Jz > basis, it gives the wrong result, the signs on the terms that appear in > JzKet(1,0).rewrite("Jx") are switched. This is likely me messing up the > Euler angles or the invoking of the D-function. What is implemented is > rewrite, which rewrites states in terms of a new basis. For example, we > would expect: > >>>JzKet(1, 0).rewrite("Jx") > sqrt(2)/2*|1, 1>-sqrt(2)/2*|1, -1> > Note that the output kets are JxKet's, the printing of this is currently > ambiguous. > Concerning the printing you can see what I propose here https://github.com/sympy/sympy/pull/186 This pull request is a mess. I should squash many of the commits, but the diffs are clear. > >>>from sympy.physics.quantum.innerproduct import InnerProduct > >>>Innerproduct(JxBra(1,1), JzKet(1,0)).doit() > sqrt(2)/2*|1, 1> > Both of these functions, however, rely on represent, which gives the > transformed state as a vector in terms of the basis elements of the new > basis, so > >>>from sympy.physics.quantum.represent import represent > >>>represent(JzKet(1,0), basis=Jx) > [ sqrt(2)/2] > [ 0] > [-sqrt(2)/2] > Represent invokes Note that the statement from > above, qapply(JzBra(1,1)*JzKet(1,1).rewrite('Jx')), qapply automatically > turns the multiplication into an innerproduct and evaluates it. Tomorrow > morning, I'll be putting in some docstrings to make the usage of this clear > and opening a pull request for this branch, any review as to the > implementation of the Wigner D-function would be a great help. > > Let me know if you have any questions or see any issues. Thanks. > > Sean > > [0] https://github.com/flacjacket/sympy/tree/xyz_bases > [1] http://code.google.com/p/sympy/issues/detail?id=2423 > [2] > http://www.chem.ucsb.edu/coursepages/11spring/226-Metiu/dl/115A%20Course%20Notes/Ch11_Angular_20Nov09.pdf > page > 23 > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/sympy?hl=en. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
