= 5.5 The one-dimensional parity operator II is defined by П(x) (-x). In other words, II changes x into -x everywhere in the function. (a) Is II a Hermitian operator? (b) For what potentials V(x) is it possible to find a set of wavefunc- tions which are eigenfunctions of the parity operator and solutions of the one-dimensional time-independent Schrödinger equation?

goes from - to +∞. 18. Normalize the wavefunction, = (2-)e and find and . 2018

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Legrende polynomials The amplitude of a stray wave is defined by: SO) =x (21+ 1) exp li8,] sen 8, P(cos 8). INO Here e is the scattering angle, / is the angular momentum and 6, is the phase shift produced by the central potential that performs the scattering. The total cross section is: Show that: 'É4+ 1)sen² 8, .

how do i do a? I sit by finding the constant = 1? Pls help me

P7E.11 The expectation value of the kinetic energy of a harmonic oscillator is most easily found by using the virial theorem, but in this Problem you will find it directly by evaluating the expectation value of the kinetic energy operator with the aid of the properties of the Hermite polynomials given in Table 7E.1. (a) Write the kinetic energy operator T in terms of x and show that it can be rewritten in terms of the variable y (introduced in eqn 7E.7) and the frequency w as d? dy The expectation value of this operator for an harmonic oscillator wavefunction with quantum number v is d? (T),=-hwaN; ſ H,en. dy H,evirdy where N, is the normalization constant (eqn 7E.10) and a is defined in eqn 7E.7 (the term a arises from dx = ady). (b) Evaluate the second derivative and then use the property H" – 2yH, + 2vH, = 0, where the prime indicates a derivative, to rewrite the derivatives in terms of the H, (you should be able to eliminate all the derivatives). (c) Now proceed as in the text, in…

This is a problem in the field of quantum mechanics.

Check if the following operators with the corresponding functions could form an eigen value equations or not (where Bis a constant value) No. function Оperator 3 2 3 sin(ßx) sin(Bx) d dx 4 sin(ßx) dx

(AA) ²( ▲ B) ²≥ ½ (i[ÂÂ])² If [ÂÂ]=iñ, and  and represent Hermitian operators corresponding to observable properties, what is the minimum value that AA AB can have? Report your answer as a decimal number with three significant figures.

Show that the following wave function is normalized. Remember to square it first. Limits of integration go from -infinity to infinity. DO NOT SKIP ANY STEPS IN THE PROCEDURE