1. Show that the function (x) = 6x³ is an eigenfunction of the operator А = X What is the corresponding eigenvalue? d dx
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Q: Q2. If you are given the following operator 03, acts on function of position 4(x). as: O34(x) = v(x)…
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Q: 4. Let T be the time reversal operator. Show that T-U*K where U is the unitary operator and K is the…
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Q: 1. Find the Matrix that represents the operator of the second derivative with respect to position.…
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Q: 5. Consider the following wavefunctions. Determine which are eigenfunctions of each operator listed.…
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Q: 1. Following is a 1D wavefunction that is associated with a particle moving between -o and +oo: (x)…
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Q: (b) f(x) = Acos(ax), = d2/dx2, where A and a are constants (c) f(x) = Ae-ax,…
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Q: Show that AA for any operator A is positive. Â
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- 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 O0 A physical system is described by a two-dimensional vector space with Hamiltonian operator Ĥ given by Ĥ = (_) where a is a constant. At time t = 0, the system is prepared in state (t = 0)) = -i2.5 0 determine the expectation value (Ŝ) at time t = πħ/(4x). O a. 2.17 O b. -2.50 O c. -1.25 O d. 2.50 O e. 5.00 0 (¹). For operator $ = (2 i2.5