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Show that it satisfies the following properties: Anticommutativity {f,g} = -{9, f} Bilinearity {af + bg, h} = a{f,h} + b{g,h}, {h, af + bg} = a{h, f}+b{h, g}

Show that it satisfies the following properties: Anticommutativity {f,g} = -{9, f} Bilinearity {af + bg, h} = a{f,h} + b{g,h}, {h, af + bg} = a{h, f}+b{h, g}

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It's a quantum mechanics question.

Show that it satisfies the following properties: Anticommutativity {f,g} = -{9, f} Bilinearity {af + bg, h} = a{f,h} + b{g,h}, {h, af + bg} = a{h, f}+b{h, g}
Transcribed Image Text:Show that it satisfies the following properties: Anticommutativity {f,g} = -{9, f} Bilinearity {af + bg, h} = a{f,h} + b{g,h}, {h, af + bg} = a{h, f}+b{h, g}
Expert Solution
Step 1

 

Given,

f,g=∑i∂xif ∂pig-∂pif ∂xig       ..........1

Anticommutativity:

Now by definition,

g,f=∑i∂xig ∂pif-∂pig∂xif=-∑i∂xif ∂pig-∂pif ∂xig  =-f,g     From1

Thus,

f,g=-g,f

 

 

 

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