Consider a weakly anharmonic a 1D oscillator with the poten- tial energy U(2) = u² + Br* Calculate the energy levels in the first order in the small anharmonicity parameter 3 using TIPT and the ladder operators.
Q: Solve the time independent Schrodinger equation for a particle with mass m and energy 0 < E < V1 for…
A:
Q: Minimize the expectation value of the hamiltonian for the one dimensional quantum oscillator using…
A: Sure, The minimization of the expectation value of the Hamiltonian for the one-dimensional quantum…
Q: Use the ground-state wave function of the simple har- monic oscillator to find x, (x²), and Ax. Use…
A:
Q: What is the first excited state energy for a square well potential (with V = -10 hartrees and a…
A: Given, V= -10 hartrees width of -1 < x < 1
Q: Solve the 3-dimensional harmonic oscillator for which V(r) = 1/2 mω2(x2 + y2 + z2), by the…
A:
Q: Derive an expression for the Helmholtz free energy of a single harmonic oscillator, whose energy…
A: Step 1: When the oscillator can be treated quantum mechanicallyQuantum mechanically the energy…
Q: Show that ? (x,t) = A exp [i (kx - ?t] is a solution to the time-dependent Schroedinger equation for…
A:
Q: Using the eigenvectors of the quantum harmonic oscillator, i.e., |n >, find the matrix element…
A: Given, Maxtrix element of momentum operator for harmonic quantum oscillator
Q: Consider a potential barrierV(x) = {0, xVo, find the transmission coefficient, T
A:
Q: A harmonic oscillator is prepared in a state given by 2 1/3/53 01 0(0) + / 390,0 (x) y(x) = - 'n…
A: The expectation value of energy for a normalized wave function is given by the formula, E=ψ|En|ψ…
Q: A system is in an eigenstate |m, l) of the angular momentum operators L2 and L2. Calculate the…
A:
Q: A particle of mass m is constrained to move between two concentric impermeable spheres of radii r =…
A:
Q: By direct substitution, show that the wavefunction in the figure satisfies the timedependent…
A:
Q: The odd parity eigenstates of the infinte square well , with potential V = 0 in the range −L/2 ≤ x ≤…
A:
Q: The classical turning points of a harmonic oscillator occur at the displacements at which all of the…
A: The energy of the oscillatoe for state ν=0 is given byNow equating this energy with potential…
Q: A system is in the state = m, an eigenstate of the angular momentum operators L² and L₂. Calculate…
A:
Q: Consider an infinite well, width L from x=-L/2 to x=+L/2. Now consider a trial wave-function for…
A:
Q: Apply variational method to simple harmonic oscillator . Use different trial wavefunctions and…
A: Taking an exponentially decreasing trail wavefunction: ψ(x)=Ae-βx
Q: Suppose you measure A with eigenvalues A1, 2, and X3 with corresponding eigenvectors |1), |2), and…
A: Solution: Given that, Normalized wave function (ψ)=α |1>+β|2>+γ|3>
Q: Write the possible (unnormalized) wave functions for each of the fi rst four excited energy levels…
A: for cubical box,Lx=Ly=Lz=Land wave function ψ(x,y,z)=AsinnxπLxsinnyπLysinnzπLz
Q: For a simple harmonic oscillator particle exist up to the second excited state (n=2) what is the…
A: Given: The properties of the ladder operator are
Q: A proton is confined in box whose width is d = 750 nm. It is in the n = 3 energy state. What is the…
A:
Q: PROBLEM 2 Calculate the probability distribution of momenta p for a ld oscillator in the ground…
A: Solution: The ground state is n =0. The position and momentum operator in terms of raising and…
Step by step
Solved in 3 steps with 3 images
- For a particle, the unperturbed states are with the allowed (dimensionless) energies = 0, +1, +2, .... If we introduce the perturbation Hamiltonian Â' such of n², where n = that: 0.5 0.2 0 for k=1 and g = -1 for k=g = 0 0.3 ) Find the (dimensionless) first order correction to the ground state energy for k= g = 1 for k=g = −1 (Y|A|) =Consider an electron in a 2D harmonic trap with force constants kxx = 232 N/m and kyy = 517 N/m. List the energies of the lowest 10 eigenfunctions.Show that ? (x,t) = A cos (kx - ?t) is not a solution to the time-dependent Schroedinger equation for a free particle [U(x) = 0].
- Evaluate the E expressions for both the Classical (continuous, involves integration) and the Quantum (discrete, involves summation) models for the energy density u, (v).consider an infinite square well with sides at x= -L/2 and x = L/2 (centered at the origin). Then the potential energy is 0 for [x] L/2 Let E be the total energy of the particle. =0 (a) Solve the one-dimensional time-independent Schrodinger equation to find y(x) in each region. (b) Apply the boundary condition that must be continuous. (c) Apply the normalization condition. (d) Find the allowed values of E. (e) Sketch w(x) for the three lowest energy states. (f) Compare your results for (d) and (e) to the infinite square well (with sides at x=0 and x=L)Prove in the canonical ensemble that, as T ! 0, the microstate probability ℘m approaches a constant for any ground state m with lowest energy E0 but is otherwise zero for Em > E0 . What is the constant?