Show that the function y = cos(4x) Is an eigen function for this operator d? Â = dx2
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A: Since you have have asked multiple question, we will solve the first question for you. If you want…
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- Under what conditions will a linear operator L̑ on a function space be Hermitian?Draw the symbol of the logic gate that implements the following Boolean expression in the image attached: ? ⊕ ?, and show its truth table.O Consider the kinetic energy matrix elements between Hydrogen states (n' = 4, l', m'| |P|²| m -|n = 3, l, m), = for all the allowed l', m', l, m values. What kind of operator is the the kinetic energy (scalar or vector)? Use this to determine the following. For what choices of the four quantum numbers (l', m', l, m) can the matrix elements be nonzero (e.g. (l', m', l, m) (0, 0, 0, 0),...)? Which of these nonzero values can be related to each other (i.e. if you knew one of them, you could predict the other)? In this sense, how many independent nonzero matrix elements are there? (Note: there is no need to calculate any of these matrix elements.)
- Show that the operator H = -1/2(d^2/dx^2) is hermitian, assuming that it operates on a Hilbert space of L^2 functions whose functions and derivatives vanish at x = −∞ and x = +∞In the operator eigenvalue equation, Af(x) =a f(x), which of the following statements is not true? the effect of the operator, A, on f(x) is to increase its magnitude by a factor of a Omultiples of f(x) would be eigenfunctions of the operator, A Of(x) is an eigenfunction of the operator, A the number, a, must be equal to 0 or 1 OOO O