The energy spectrum of a bound state is None of the above Discrete O Continuous but with some missing lines Continuous
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- Explain the energy level splitting of the Zeeman effect.Particle of mass m moves in a three-dimensional box with edge lengths L1, L2, and L3. (a) Find the energies of the six lowest states if L1 =L, L2 = 2L, and L3 = 2L. (b) Which if these energies are degenerate?For an infinite potential well of length L, determine the difference in probability that a particle might be found between x = 0.25L and x = 0.75L between the n = 3 state and the n = 5 states.
- 7. Consider a particle in an infinite square well centered at x = 0 in one of its stationary states. For this problem, you may look up any integrals. Some useful ones are given in Harris. a) Compute (x) and (pr) for arbitrary n. Do this by direct computation but then describe how you could have found these results using symmetry (the symmetry can either be symmetry in the physical system, such as the shape of the wave function, or symmetry related to the expectation value integral, such as the shape of the integrand). b) Using your answer to part a), show that the uncertainty in the momentum is Apx nh for arbitrary n. Do this two ways: (i) first by using your answer to part a) and directly computating (p2) (via an integral) and (ii) by using your answer to part a) and relating (p2) to the kinetic energy operator. c) Show that the uncertainty principle holds for the ground state. 2L -Calculate the probability that for the 1s state the electron lies between r and r+drWhat result is the most likely to find a particle that has the state function y(x) as shown below? X₁ (b) x₂ (c) xc (d) None Jantes
- A particle is in a three-dimensional cubical box that has side length L. For the state nX = 3, nY = 2, and nZ = 1, for what planes (in addition to the walls of the box) is the probability distribution function zero?a 4. 00, -Vo, V(z) = 16a 0, Use the WKB approximation to determine the minimum value that V must have in order for this potential to allow for a bound state.Consider an electron trapped in a 20 Å long box whose wavefunction is given by the following linear combination of the particle's n = 2 and n = 3 states: ¥(x,t) =, 2nx - sin ´37x - sin 4 where E, 2ma² a a. Determine if this wavefunction is properly normalized. If not, determine an appropriate value for a normalization constant. b. Show that this is not an eigenfunction to the PitB problem. What are the possible results that could be returned when the energy is measured and what are the probabilities of measuring each of these results?