- #1

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[tex] [x_i , p_i ^n p_j^m p_k^l] [/tex]

I could apply a test function g(x,y,z) to this and get:

[tex]=x_i p_i ^n p_j^m p_k^l g - p_i ^n p_j^m p_k^l x_i g [/tex]

but from here I'm not sure where to go. any help would be appreciated.

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- Thread starter indigojoker
- Start date

- #1

- 246

- 0

[tex] [x_i , p_i ^n p_j^m p_k^l] [/tex]

I could apply a test function g(x,y,z) to this and get:

[tex]=x_i p_i ^n p_j^m p_k^l g - p_i ^n p_j^m p_k^l x_i g [/tex]

but from here I'm not sure where to go. any help would be appreciated.

- #2

Gokul43201

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You don't need a test function. All you need are the following:

(i) [itex] [x_i,p_j] = i \hbar \delta_{i,j} [/itex]

(ii) [itex] [AB,C]=A[B,C]+[A,C]B [/itex]

(i) [itex] [x_i,p_j] = i \hbar \delta_{i,j} [/itex]

(ii) [itex] [AB,C]=A[B,C]+[A,C]B [/itex]

Last edited:

- #3

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should that be [itex] [x_i,p_j] = i \hbar \delta_{i,j} [/itex]?

- #4

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i guess a more reasonable question would i expand [itex][x_i,p_i^n][/itex]

- #5

Gokul43201

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Try p^2 and p^3 first - you'll see what I mean.

PS: Yes, there was a "bad" minus sign which I've now fixed.

- #6

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how about: [itex][x_i,p_i^n]=ni \hbar p_i ^{n-1} [/itex]

- #7

Gokul43201

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Looks good. Now you're just a step or two away from the answer to the original question.

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