Calculate the commutator [p x , x[SUP]n[/SUP]]

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SUMMARY

The discussion focuses on calculating the commutator [px, xn] and includes tasks involving the kinetic energy operator Kx defined as Kx = - (ħ²/2m)(d²/dx²). Participants are tasked with calculating the commutators [x, Kx] and [px, Kx]. The commutation relations are essential for understanding quantum mechanics and the behavior of operators in this context.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with commutators and their significance
  • Knowledge of the kinetic energy operator in quantum mechanics
  • Basic calculus, particularly differentiation
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  • Study the properties of commutators in quantum mechanics
  • Learn about the implications of the kinetic energy operator Kx
  • Explore the calculation of higher-order commutators
  • Investigate the role of operators in quantum state transformations
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Students of quantum mechanics, physicists working with operator algebra, and anyone involved in advanced theoretical physics calculations.

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Calculate the commutator [px, xn]

Homework Statement



There are 3 tasks.
1) No other information is given. only that I have to calculate the commutator [px, xn].

For task 2 and 3 a relevant equation is given below.

2) calculate the commutator [x, Kx]

3) calculate the commutator [px, Kx]

Homework Equations



We define the kinetic energy operator of a particle in one dimension (x) as

Kx = - (h(hatch)2/2m)(d2/dx2)

I hope anyone can help me. I am really stuck with these commutators.

- HP
 
Physics news on Phys.org
Try multiplying the commutator at the right by some phantom ket |K>...
 

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