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What Is the Position Operator if Momentum Is Given by a Specific Operator?
If [A, B] = 1 then [A, A + B] = 1 [A, A + B] = A(A + B) - (A + B)A = AA + AB - AA - BA = AB - BA = [A, B] = 1 We have p = c(A + B) and [x, p] = iħ. xp - px = iħ cx(A + B) - c(A + B)x = iħ x(A + B) - (A + B)x = iħ/c | multiply on A from the left Ax(A + B) - A(A + B)x = iħ/c A | A(A + B)...- kemiisto
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- Forum: Advanced Physics Homework Help
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What Is the Position Operator if Momentum Is Given by a Specific Operator?
Homework Statement Find the operator for position x if the operator for momentum p is taken to be \left(\hbar/2m\right)^{1/2}\left(A + B\right), with \left[A,B\right] = 1 and all other commutators zero. Homework Equations Canonical commutation relation \left [ \hat{ x }, \hat{ p } \right ] =...- kemiisto
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- In quantum mechanics Mechanics Operators Quantum Quantum mechanics
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- Forum: Advanced Physics Homework Help