*Problem 1.5 Consider the wave function ¥(x. t) = Ae¬lx1e-iwr, where A, 2, and w are positive real constants. (We’ll see in Chapter 2 what potential (V) actually produces such a wave function.) (a) Normalize ¥. (b) Determine the expectation values of x and x2. 12A good mathematician can supply you with pathological counterexamples, but they do not arise in physics: for us the vave function always goes to zero infinity at

Just need problem 4

Figure 1.12 shows an exemplary oscilloscope screen with two harmonic waveforms. CH 1 Offset: -3 V I | | I 1 V/div CH 2 Offset: 2 V 2 V/div 10 μs/div Figure 1.12: Two harmonic waveforms on an oscilloscope screen.

slove part 2

Assistance with last two questions

QUESTION 1 The expectation value is the strict average of the possible values. O True False

Use your generic solution to the 2D box wavefunctions to demonstrate the following prop- erties of wavefunctions. 1. Show that if you independently normalize (x) and (y) that the product of (x) and (y) is also normalized. 2. Show that the wavefunctions for one dimension are orthogonal. Orthogonality means that f₁ Vndr = Smn, where the Kroenecker delta function means that the function is one for men and zero for m‡n. m 3. How many quantum numbers are needed to describe the energy of your system? 4. Show that the two dimensional wavefunctions are orthogonal by performing this test on the wavefunction for n = 1, ny = 2 and the wavefunction for nr = 2 and ny = 1. CLx Ly Mathematically the operations looks like f¹* f¹¹ V₁,2 (x, y) V2,1 (x, y) dxdy.

Problem #2 Calculate the Legendre transform (F1) of y = x². For your answer, give the new function F1 and its derivative dF1. (a(f(x)) Note that dy = C dx, C, = f(x), and dC, = (0) dx. dx

PHET Simulation - Wave on a String Submit Previous Answers v Correct The effect of damping is akin to the absorbance or partial reflection of light, whore the amplitude of in phase photons becomes reduced. Part B Reset the PHET simulation (using the button in the lower tight) and set it up in the following manner select Oscillate, select No End, and use the parameters in parentheses by sliding the bars for Amplitude (1.00 cm). Frequency (2.00 Hz). Damping (none), and Tension (highest) Using the available Rulers, calculate the frequency of a photon that corresponds to the wavelength of the resulting wave. Assume the length with umits (cm) of the ruler represents the real photon wavelength and that the spced of light is 3.00 x 10° m/s. Express the frequency in hertz to two significant figures. > View Available Hint(s) ΑΣφ frequency= Hz Submit Part C Complete previous part(s) 452 PM P Type here to search Fi 322021

please solve number 4