Find the ground-state energy and wave function of a system of N identical non-interacting particles confined in a one-dimensional infinity well when the particles are (a) bosons and (b) fermions with spin 1/2
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- Consider a system in a state Y If the x component of 2, m angular momentum L is measured on it, find the possible values the measurement will yield and their correponding probabilities.1Consider a one-dimensional infinite well of width w along the z-axis. Find the ground state energy and wave function of a system of N noninteracting identical particles that are confined to when the particles are bosons and spin 1/2 fermions.
- A particle is initially prepared in the state of = [1 = 2, m = −1 >|, a) What's the expectation values if we measured (each on the initial state), ,, and Ĺ_ > b) What's the expectation values of ,, if the state was Î_ instead?(b) Suppose a particle trapped in an one-dimensional box of width a with infinitely hard walls. Derive the normalized wave function from the solution of wave function? Find the probability of particle that can be found between 0.4a and 0.5a for the first excited state.make a quantum scheme that performs the addition of a pair of two-qubit numbers x and y modulo 4: |x, y> → |x, x + y mod 4>
- Please asapConsider a weakly anharmonic a 1D oscillator with the poten- tial energy m U(x) = w?a² + Ba* 2 Calculate the energy levels in the first order in the small anharmonicity parameter 3 using TIPT and the ladder operators.Sketch the expected occupation number for a state with energy ε as a function of the temperature T when the particles are (i) bosons or (ii) fermions, and explain how these simplify when the system is dilute.
- Is exp(-x) a wave function or not?Suppose you have three particles, and three distinct one-particle states (Va(x), Vb(x), and ye(x)) are available. How many different three-particle states can be constructed, (a) if they are distinguishable particles, (b) if they are identical bosons, (c) if they are identical fermions? (The particles need not be in different states-Wa(x1)¥a(x2)ựa (.x3) would be one possibility, if the particles are distinguishable.) |