Answered: The Hamiltonian of a particle having… | bartleby

Related questions

Question

The Hamiltonian of a particle having mass m in one dimension is described by
p²1
+-mox +2µx. What is the difference between the energies of the first two
H
2m 2
levels?
2µ²
(а) ho-
mo?
(b) ħo+µ
(с) hо
(d) ho+-
mo?

Expert Solution

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Problem 6: A uniform wooden meter stick has a mass of m = 763 g. A clamp can be attached to the measuring stick at any point P along the stick so that the stuck can rotate freely about point P, which is at a distance d from the zero-end of the stick as shown. Randomized Variables m = 763 g 1 2 3045 6 7 12 13 14 15 16 17 18 10 11 Otheexpertta.com
Consider the function v(1,2) =( [1s(1) 3s(2) + 3s(1) 1s(2)] [x(1) B(2) + B(1) a(2)] Which of the following statements is incorrect concerning p(1,2) ? a. W(1,2) is normalized. Ob. The function W(1,2) is symmetric with respect to the exchange of the space and the spin coordinates of the two electrons. OC. y(1,2) is an eigenfunction of the reference (or zero-order) Hamiltonian (in which the electron-electron repulsion term is ignored) of Li with eigenvalue = -5 hartree. d. The function y(1,2) is an acceptable wave function to describe the properties of one of the excited states of Lit. Oe. The function 4(1,2) is an eigenfunction of the operator S,(1,2) = S;(1) + S,(2) with eigenvalue zero.
please answer c) only 2. a) A spinless particle, mass m, is confined to a two-dimensional box of length L. The stationary Schrödinger equation is - +a) v(x, y) = Ev(x, y), for 0 < r, y < L. The bound- ary conditions on ý are that it vanishes at the edges of the box. Verify that solutions are given by 2 v(1, y) sin L where n., ny = 1,2..., and find the corresponding energy. Let L and m be such that h'n?/(2mL²) = 1 eV. How many states of the system have energies between 9 eV and 24 eV? b) We now consider a macroscopic box (L of order cm) so that h'n?/(2mL?) ~ 10-20 eV. If we define the wave vector k as ("", ""), show that the density of states g(k), defined such that the number of states with |k| between k and k +dk is given by g(k)dk, is Ak 9(k) = 27 c) Use the expression for g(k) to show that at room temperature the partition function for the translational energy of a particle in a macroscopic 2-dimensional box is Z1 = Aoq, where 2/3 oq = ng = mk„T/2nh?. Hence show that the average…
Activity 7 (a) Solve the following equations for real x and- (i) 3+5i+x-yi = 6 – 2i (4*3 (ii) x+yi=(1-i)(2+8i). (b) Determine the complex number z which satisfies z(3+3i) = 2-i.
c) How does the classical kinetic energy of the free electron compare in magnitude with the result you obtained in the previous part?
24. Consider a modified box potential with V(x) = V₁x, Vi(ar), x a Use the orthogonal trial function = c₁f₁+c₂f₂ with f₁ = √√sin (H) and f2 = √√ √√sin sin (2) to determine the upper bound to ground state energy.