Timeline for How to put the tensor product of two operators onto two variables?
Current License: CC BY-SA 3.0
11 events
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| May 7, 2015 at 8:38 | comment | added | user14634 | Would you please help me on this new question: mathematica.stackexchange.com/questions/82778/…, Thanks a lot! | |
| Feb 12, 2015 at 10:22 | history | edited | Mr.Wizard | CC BY-SA 3.0 |
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| Sep 3, 2014 at 7:45 | comment | added | user14634 | Thank you so much! This function is really useful. | |
| Sep 2, 2014 at 12:24 | comment | added | Stephen Luttrell |
You use Coefficient to extract coefficients from expressions. So, using the state[spin, index] notation in my original answer, the probability of position -1 is #.Conjugate[#]&[Coefficient[yourstate, {state["\[DownArrow]", -1], state["\[UpArrow]", -1]}]], where the pure function #.Conjugate[#]& computes this probability from the individual basis state amplitudes.
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| Sep 2, 2014 at 9:58 | comment | added | user14634 | Thanks a lot for your good suggestion. I have succeesfully gotten the order I need. Furthermore, I need to extract the coefficient of each term, so as to plot a figure of positions VS probabilities (probability= square of the coefficient). In the above example, the probability for position -1 is (-2/(2 Sqrt[2]))^2+(1/(2 Sqrt[2]))^2. Do you have some suggestions for picking up the coefficients? I have tried several commands in Mathematica, but not succeed. Thank you very much! | |
| Aug 30, 2014 at 20:57 | comment | added | Stephen Luttrell |
You can display the results in the form that you want by simply using the Notation package (that I mentioned in my answer above) to map each internal state[index, spin] expression to your required state[spin, index] displayed output. You then get the best of both worlds - convenient internal computations AND convenient displayed output - with the Notation package connecting the two of these together.
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| Aug 30, 2014 at 14:14 | comment | added | user14634 | Thanks a lot! But I need to keep the form of state[spin,index], so as to show the original physical meaning. Would you please make a high-level program to rearrange the element? Thank you very much! | |
| Aug 30, 2014 at 10:48 | comment | added | Stephen Luttrell |
The easiest way to get the ordering you want is to define the basis state as state[index, spin] rather than state[spin, index], and to correspondingly adjust the definitions of how the H and S operators act on these basis states. Don't forget to remove the old definitions first, or start with a fresh kernel. Mathematica will then automatically display the result ordered as you want it to be.
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| Aug 30, 2014 at 9:06 | comment | added | user14634 | I have a further question: How to rearrange the element in an increasing order of the “index”? e.g., (-state["[DownArrow]", -3] - 2 state["[DownArrow]", -1] + state["[DownArrow]", 1] + state["[UpArrow]", -1] + state["[UpArrow]", 3])/(2 Sqrt[2]) is rearranged as (-state["[DownArrow]", -3] - 2 state["[DownArrow]", -1] + state["[UpArrow]", -1] + state["[DownArrow]", 1] + state["[UpArrow]", 3])/(2 Sqrt[2]) | |
| Aug 30, 2014 at 8:21 | vote | accept | user14634 | ||
| Aug 29, 2014 at 13:25 | history | answered | Stephen Luttrell | CC BY-SA 3.0 |