Physics
Physics, 03.07.2019 02:30, lexybellx3

If a and b are hermitian operators, prove that (1) the operator of ab is only hermitian if a and b commute, and (2) the operator (a+b)" is hermitian

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Physics, 29.06.2019 20:30, vannitling12p4w44f
(a) what is the condition on operator so that it is hermitian? (b) lf q is hermitian show that (ψ i q ψ) is real, for any ψ.belongs to hilbert space. (c) is the eigenvalue λ of the hermitian operator q real? prove your answer. (d) if q ψ'n = 5 and q ψ'm = 5 ψ'm, show that ψ are orthogonal.
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Physics, 11.07.2019 00:20, Wolfgirl2032
Consider two operators \hat{a} and \hat{b}. the operation \hat{a}\hat{b} |ψ> means first operate on state |ψ> with operator \hat{b} to produce a new state |φ> ≡ \hat{b} |ψ> , then operate on the new state |φ> with operator \hat{a} to produce yet another state |φ'> ≡ \hat{a} |φ> , i.e. |φ'> = \hat{a} |φ> = \hat{a}\hat{b} |ψ> . note that, in general, the order of operation matters, i.e., \hat{a}\hat{b}\neq\hat{b}\hat{a} (aˆ and bˆ do not commute). (a) using the definition that the hermitian adjoint of aˆ |ψ> is < ψ| \hat{a}^\dagger , prove that (aˆbˆ)^† = bˆ†aˆ† . (b) suppose that aˆ and bˆ are both hermitian and that they do not commute aˆbˆ \neq bˆaˆ. is the product aˆbˆ hermitian? is the sum of products aˆbˆ + bˆaˆ hermitian? (c) suppose that aˆ and bˆ are both hermitian and that they commute aˆbˆ = bˆaˆ. is the product aˆbˆ hermitian? you for any that you can
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