larry stead

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These are questions asked by larry stead

simp.mw

please see simp.mw file

restart

with(Physics)

Setup(spacetime)

[spacetimeindices = greek]

(1)

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 1142 and is the same as the version installed in this computer, created 2022, February 12, 11:16 hours Pacific Time.`

(2)

Define(t[mu])

{Physics:-Dgamma[mu], Physics:-Psigma[mu], Physics:-d_[mu], Physics:-g_[mu, nu], t[mu], Physics:-LeviCivita[alpha, beta, mu, nu]}

(3)

NULL

SumOverRepeatedIndices(t[mu]*t[`~mu`])

t[1]*t[`~1`]+t[2]*t[`~2`]+t[3]*t[`~3`]+t[4]*t[`~4`]

(4)

NULL

SumOverRepeatedIndices(t[mu]*t[`~mu`])

t[1]*t[`~1`]+t[2]*t[`~2`]+t[3]*t[`~3`]+t[4]*t[`~4`]

(5)

NULL

SumOverRepeatedIndices(t[mu]*t[`~μ`])

t[mu]*t[`~μ`]

(6)

NULL

Download greek-index.mw

I am trying to do matrix multiplication with Dirac gamma matrices, but am getting a recursion error. 

the final input line, which is causing the error, doesn't seem to be inserted, but it is:

Library:-PerformMatrixOperations((mt . (Dgamma[2])) . m)

can anybody tell me what i'm doing wrong? i don't understand why 

Dgamma[2] . m 

works but 

mw . Dgamma[2] . m 

gets the recursion error. 

then i saw something that made me think i needed to use 'matrix', instead of 'Matrix'. so i tried that(gamult2) - now the 2nd multiply works, and the first fails.

any help greatly appreciated!

thanks,

larry

restart

with(Physics)

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 452 and is the same as the version installed in this computer, created 2019, October 23, 13:26 hours, found in the directory /Users/lstead/maple/toolbox/2019/Physics Updates/lib/`

(1)

with(LinearAlgebra)

``

m := Matrix(4, 1, {(1, 1) = 1, (2, 1) = 2, (3, 1) = 3, (4, 1) = 4})

Matrix(%id = 18446744078528784254)

(2)

mt := Transpose(m)

Matrix(%id = 18446744078392267830)

(3)

mt.m

Matrix(%id = 18446744078392260238)

(4)

Library:-PerformMatrixOperations(Dgamma[2].m)

Matrix(%id = 18446744078528770526)

(5)

Library:-PerformMatrixOperations(mt.Dgamma[2].m)

Error, (in Physics:-GetDefineINFO) too many levels of recursion

 

``


 

Download gammult.mw

gammult2.mw

hi,

I want to setup quantum mechanical angular momentum operators and kets such that i can do something like:

Lz[2] . Ket(??, j, m) -> m hbar        (instead of getting m as eigenvalue)

L^2[1] . Ket(??, j, m) -> j (j+1) hbar^2           (instead of getting j)

where L and Lz are quantum operators. 

maybe if i knew how to do 

QuantumOp . Ket{QuantumOp, j) -> j (j+1)

i could do it with explicit tensor products of Kets - one for j, one for m?

can somebody give me an idea of how to do this, or point me at an example?

many thanks,

larry

is there a way to have output left justified, instead of centered?

in other words, i want this:

 

4-1

3

 

not the normal

4-1

                                                                 3

 

thanks

 

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