Find the average value on the interval [2,5] of the function whose graph appears below. average value = 3. 1. 1 5 6 4. 3.
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- 40. The first excited state of the harmonic oscillator has a wave function of the form y(x) = Axe-ax². (a) Follow theA real wave function is defined on the half-axis: [0≤x≤00) as y(x) = A(x/xo)e-x/xo where xo is a given constant with the dimension of length. a) Plot this function in the dimensionless variables and find the constant A. b) Present the normalized wave function in the dimensional variables. Hint: introduce the dimensionless variables = x/xo and Y(5) = Y(5)/A.Show that the one-particle partition function Z₁ for a 2D ideal gas confined to area A is: A 2²/1 Z₁ = S
- For T = 0.3 sec, write the element of the discrete sequence corresponding to the function f(t) = 5t with k = 18. Provide your answer in seconds to the nearest first decimal place. Pay attention to the numbers given4. a) Consider a square potential well which has an infinite barrier at x = 0 and a barrier of height U at x = L, as shown in the figure. For the case E L) that satisfy the appropriate boundary conditions at x = 0 and x = o. Put the appropriate conditions on x = L to find the allowed energies of the system. Are there conditions for which the solution is not possible? explain. U E L.