3 Consider a system of eight non-interacting, identical quantum particles of spin- in a 2 one dimensional box of length L. The minimum excitation energy of the system, in units of is 2mL?
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- A particle in a 3-dimensional quadratic box with box length L has an energy given by h² E = (n+n+n). The degeneracies of the first, second, and 8mL² third level are a. e. 1, 2, 3 1, 3, 3 b. 1, 3, 1 c. 3, 3, 3 d. 1, 2, 24. Find the points of maximum and minimum probability density for the nth state of a particle in a one- dimensional box. Check your result for the n=2 state.2. A wave function is a linear combination of 1s, 2s, and 3s orbitals: y(r) = N(0.25 y,s + 0.50W2, +0.30W). Find the normalization constant N, knowing that 1s, 2s, and 3s orbitals are normalized.
- 3. For free particles in two dimensions, what is density of states (DOS) in low speed limit (=p²/2m), and in high speed limit (=pc)?7. One electron is trapped in a one-dimensional square well potential with infinitely high sides. a. If you have a probe that has a width for electron detection Ax = 0.00350L in the x direction, for the first excited state ( n =2), what is the probability that the electron is found in the probe when it is centered at x = L/4, (hint: you can use an approximation for this - you do not need to do an integral)? b. What is the average number of electrons that you would detect using the probe described in part "b." centered at x = L/4, ifthe electron is in the first excited state (n = 2) for each experiment and you repeat the experiment N, =100,000 times?5