Answer the following about an observable that is represented by the operator  = wo (3² + 3²). ħ (4) Is it possible to write a complete set of basis states that are simultaneously eigenstates of the operator Ĵ and Â? If so, explain how you know. If not, write an uncertainty principle for the observables A and J.
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- i li. 9 V:OV docs.google.com/forms/d/e Which function is preferable to find the magnitude of a complex number? * sqrt() cart2pol() MATLAB does not support complex arguments abs() All matrices are vectors but all vectors are not matrices in MATLAB * False True Compute 24 modulo 5. b = mod(24,5) * b =6 b =4 b =5 b = 3 O OConsider the function v(1,2) =( [1s(1) 3s(2) + 3s(1) 1s(2)] [x(1) B(2) + B(1) a(2)] Which of the following statements is incorrect concerning p(1,2) ? a. W(1,2) is normalized. Ob. The function W(1,2) is symmetric with respect to the exchange of the space and the spin coordinates of the two electrons. OC. y(1,2) is an eigenfunction of the reference (or zero-order) Hamiltonian (in which the electron-electron repulsion term is ignored) of Li with eigenvalue = -5 hartree. d. The function y(1,2) is an acceptable wave function to describe the properties of one of the excited states of Lit. Oe. The function 4(1,2) is an eigenfunction of the operator S,(1,2) = S;(1) + S,(2) with eigenvalue zero.Use the WKB approximation to find the eigenenergies EWKB and the eigenfunctions WKB for the potential V (r) = A|r|. In what limit do you expect your answers to approach the exact results? explain.
- A particle of mass m moves non-relativistically in one dimension in a potential given by V(x) tion. The particle is bound. Find the value of ro such that the probability of finding the particle with |r| < 2o is exactly equal to 1/2. :-aố (x), where d(x) is the usual Dirac delta func-DIRECTION: Please provide a step-by-step and clear solution to each of the problems below. Z 4) Show that (7.a)² = a² 1₂, where ở = σ¸î + σ¸ĵ + σ₂â‚ ā = axî + ayĵ + a₂î, and 1₂ is the usual 2 and oz x 2 identity matrix. Further, the components ax, ay, and a are constants, and σx, y, are the Pauli spin matrices given in the previous item, Item 3.Solve the for the energy eigenvalues and eigenfunctions for a particle in a 1D box such that the box has a length L and is centered about the origin of a coordinate system. Find values of mL? such that the particle becomes relativistic, it hardly moves, or moves with the speed of an airbus in its ground state.
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- Physics Department PHYS4101 (Quantum Mechanics) Assignment 2 (Fall 2020) Name & ID#. A three-dimensional harmonic oscillator of mass m has the potential energy 1 1 1 V(x.y.2) = ; mw*x² +mwży² +=mw;z? where w1 = 2w a. Write its general eigenvalues and eigenfunctions b. Determine the eigenvalues and their degeneracies up to the 4th excited state c. The oscillator is initially equally likely found in the ground, first and second excited states and is also equally likely found among the states of the degenerate levels. Calculate the expectation values of the product xyz at time tFind an equation for the plane through the points (-6, 8, – 1) and (-1,3, –8) and perpendicular to the plane -4x – 3y + 8z = 10. An equation for the plane is ...Problem : Given the transfer function of a linear lung mechanics model S G(s) s3 + 3s2 + 2s a. Find the full-dimensional (3-D) controllable realization. b. Find a minimal realization. c. Verify the minimal realization is both controllable and observable.