18. In differential form, what is the kinetic energy operator equal to? Does this depend on the problem that you are solving in quantum mechanics? What is the eigenvalue spectrum for this operator?
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- 2. *Problem 6.9 Consider a quantum system with just three linearly independent states. The Hamiltonian, in matrix form, is 0. H = Vo 1 where Vo is a constant and e is some small number (e « 1). (a) Write down the eigenvectors and eigenvalues of the unperturbed Hamiltonian (e = 0). %3D (b) Solve for the exact eigenvalues of H. Expand each of them as a power series in E, up to second order. (c) Use first- and second-order nondegenerate perturbation theory to find the ap- proximate eigenvalue for the state that grows out of the nondegenerate eigen- vector of H. Compare the exact result from (b). (d) Use degenerate perturbation theory to find the first-order correction to the two initially degenerate eigenvalues. Compare the exact results.16. Does the linear momentum operator depend on the problem to be solved in quantum mechanics? If yes, explain why, if no, then what is it? What is the eigenvalue spectrum for this operator?Write down the role of operators in Quantum Mechanics. What happen when order of the operators is changed when they comes in product form.
- D Question 8 Can we solve the TISEq for no-particle in no boxes? No, this case does not exist in nature Yes, but only if we approximate it No, it is not part of the cases for which we can solve it Yes, but that solution is trivial and not very interesting D Question 9 The energy levels arising from the solution of the TISEq for the free particle are: Constrained Continuous Quantized Equal to the quantum number0 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