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Q: Don't used Ai solution
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Q: 63
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A: IMAGE :
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Quantum mechanics. Explain the basis of approximating the summation to an integral in translational motion.
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- What is the degeneracy of an h subshell? An n subshell?Under what conditions would the operator described as multiplication by i the square root of 1 be considered a Hermitian operator?The following operators and functions are defined: A=x()B=sin()C=1()D=10()p=4x32x2q=0.5r=45xy2s=2x3 Evaluate: a Ap b Cq c Bs d Dq e A(Cr) f A(Dq)
- For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the probability that the particle exists in the following intervals? a x=0to0.02ab x=0.24ato0.26a c x=0.49ato0.51ad x=0.74ato0.76a e x=0.98ato1.00a Plot the probabilities versus x. What does your plot illustrate about the probability?Using the original definition of the momentum operator and the classical form of kinetic energy, derive the one-dimensional kinetic energy operator K=22m2x2Let be one of the normalized eigenfunctions of a Hamiltonian operator H. Let V be an approximation of . What conditions must be satisfied by V, so that is necessarily satisfied.
- If two functions f (x ) and g (x ) are both eigenfunctions of some hermitian operator, what does it mean to say that these two eigenfunctions are degenerate?The physical interpretation of the wavefunction and the fact that it is a solution of the Schroedinger equation, which is a 2nd order differential equation, causes many restrictions on an acceptable wave function solution: (i) it must be single-valued; (ii) it must be continuous; (iii) its slope must be continuous; and (iv) it must be normalizable or normalized. Sketch the following functions and check whether they can be wave functions. Explain your answers. (Hint, it might be useful to plot the functions).First-order perturbation theory corrections to the energy require knowledge of the first-order corrected wave functions of the system. True O False
- show that the Hamiltonian operator for the total energy of a system is hermitian provided that the eigenfunction is well behavedWhat is the degeneracy of a molecule rotating with 1 = 3? With 1=4?What is antisymmetric and symmetric wave functions? Give four examples of particles having antisymmetric and symmetric symmetry. Also determine the form of the normalized antisymmetric and symmetric total eigenfunction for a system of three particles, in which the interactions between the particles can be ignored. Q. 8.
