ONLY (e) (f) NEEDED THANK YOU :)
Question 3 Consider the one-dimensional harmonic oscillator, and denote its properly normalised e...
5. Coherent States (Answer only question 5 for part a, b, and c) A coherent state is an Eigenstate of annihilation / lowering operator c) Baker- Campbell- Hausdorff Formula [Hint: Define the functions fa-eaA+8), ģ(A)-eä eABe-12 č. Note that these functions are equal at -0, and show that they satisfy the same differential equation: df/di (A+ B)f and dg/da (A+B)g Therefore, the functions are themselves equal for all λ.] A useful application of BCH formula is given in problem 5...
A particle with mass m is in a one dimensional simple harmonic oscillator potential. At timet0 it is described by the superposition state where Vo, 1 and Vz are normalised energy eigenfunctions of the harmonic oscillator potential corresponding to energies Eo, E1 and E2 (a) Show that the wavefunction is normalised (b) If an observation of energy is made, what is the most likely value of energy and with what probability would it be obtained? (c) If the experiment is...
1 From Wavefunction to Bra-Ket In bra-ket notation, a state y(x) is written as a ket: 14) + (2). The inner product between two states 41(2), 42(2) is written as a bra-ket: (441\42) = |dx (z)* #2(a). If a state is a complex linear combination |V) = a1 (41) + a2 (42), then its corresponding bra is (V= a1 (01| +a(42 In this problem, we will use the simple harmonic oscillator as a concrete example. The energy eigenstates of the...
1. Consider one-dimensional harmonic oscillator H w(aaand its energy eigenstates are denoted as ln) , n E No. The state of system is given by n-0 (a) Find Z. (b) Calculate the von Neumann entropy. (c) Evaluate mean energy.
Problem 5. (30 points) Consider a Harmonic oscillator with H that H=(ata + 1 / 2)ho, where a=dma)X + i (a) (4 points) Show P, and a x 2h 2h 2moh P. Show also 2moh that [a, a]-l. (b) (6 points) Starting from the commuters la, HJand la', A), where H-H(h) show that the eigenvalues of Hare e,=(n+1/2) for n-0, 1,2, Show also that alm)-nln-l), and a l). (( points) Find the normalized ground state wavefunction by projecting alo)-0 on...
Consider a particle with mass m described by the Hamilton operator for a one-dimensional harmonic oscillator 2 Zm 2 The normalized eigenfunctions for Hare φη (x) with energies E,,-(n + 2) ha. At time t-0 the wavefunction of the particle is given by у(x,0)- (V3іфі (x) + ф3(x)). Now let H' be an operator given by where k is a positive constant. 1) Show that H' is Hermitian. 2) Express H' by the step-operators a+ and a 3) Calculate the...
qm 2019.3 3. The Hamiltonian corresponding to the magnetic interaction of a spin 1/2 particle with charge e and mass m in a magnetic field B is À eB B. Ŝ, m where Ŝ are the spin angular momentum operators. You should make use of expres- sions for the spin operators that are given at the end of the question. (i) Write down the energy eigenvalue equation for this particle in a field directed along the y axis, i.e. B...