Study the hermitian of the E=(ih (d/dt))
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Q: Consider the following operators defined over L, (R): d = x+ dx d *** Î_ = x dx Show that Î,Î = 2.
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- (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 Q hermitian? (c) When is the product of two hermitian operators hermitian? (d) Show that the position operator (f = x) and the hamiltonian operator (H = -(h2/2m)d²/dx2? + V (x)) are hermitian.My system is a pendulum attached to moving horizontal mass m_1 and the pendulum m_2 that is shifted by X_o from origin. I have the lagrangian of my system what would be my equations of motions in terms of small angle approximation and what’s is their frequency?Calculate the hermitian conjugate (adjoins) for operator d/dx
- (AA) ²( ▲ B) ²≥ ½ (i[ÂÂ])² If [ÂÂ]=iñ, and  and represent Hermitian operators corresponding to observable properties, what is the minimum value that AA AB can have? Report your answer as a decimal number with three significant figures.The dynamics of a particle moving one-dimensionally in a potential V (x) is governed by the Hamiltonian Ho = p²/2m + V (x), where p = is the momentuin operator. Let E, n = of Ho. Now consider a new Hamiltonian H given parameter. Given A, m and E, find the eigenvalues of H. -ih d/dx 1, 2, 3, ... , be the eigenvalues Ho + Ap/m, where A is a %3|Evaluate the commutator [Â,B̂] of the following operators.