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Question related to Quantum Mechanics : Problem 3.4

Problem 3.4 (a) Show that the sum of two hermitian operators is hermitian. (b) Suppose ô is hermitian, and a is a complex number. Under what condition (on a) is a Ô hermitian? (c) When is the product of two hermitian operators hermitian? (d) Show that the position operator (x) and the Hamiltonian operator (Ĥ = -(h²/2m )d² /dx² + V (x)) are hermitian.
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Transcribed Image Text:Problem 3.4 (a) Show that the sum of two hermitian operators is hermitian. (b) Suppose ô is hermitian, and a is a complex number. Under what condition (on a) is a Ô hermitian? (c) When is the product of two hermitian operators hermitian? (d) Show that the position operator (x) and the Hamiltonian operator (Ĥ = -(h²/2m )d² /dx² + V (x)) are hermitian.
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