|U>= |D>=
|R>=|L>=
|O>=|I>=
Let U ⊆ R^n be open (not necessarily bounded), let f, g : U → R be continuous, and suppose that |f(x)| ≤ g(x) for all x ∈ U. Show that if exists, then so does . We were unable to transcribe this imageWe were unable to transcribe this image
Quantum Mechanics. Find the energies, degenerations and wave functions for the first three energy levels (ground state and first two excited states) of a system of two identical particles with spin , which move in a one- dimensional infinite well of size . Find corrections of energies to first order in if an attracting potential of contact is added. Show that in the case of "spinless" fermions, the previous perturbation has no effect. Step by step process with good handwriting,...
Quantum Mechanics. Find the energies, degenerations and wave functions for the first three energy levels (ground state and first two excited states) of a system of two identical particles with spin , which move in a one- dimensional infinite well of size . Find corrections of energies to first order in if an attracting potential of contact is added. Show that in the case of "spinless" fermions, the previous perturbation has no effect. Step by step process with good handwriting,...
Metric: slopes of light in u,r plane: or Question : In the u,r plane, show that r=R is a horizon with opposite characteristics. i.e. light rays starting at r > R cannot enter the r < R region. (This is because of the accelerating expansion of the universe) We were unable to transcribe this imageCOnstant We were unable to transcribe this image COnstant
1) Compute (Stot) and (Stt tot 2 2) Show that: Stot 2 in the basis I.,W , Ih,%) , 11., , 11.,%)} 3) Suppose that the Hamiltonian for two interacting spins is given by for some interaction strength α. Express the Hamiltonian in the operator, U, in the same basis. basis, and calculate the time evolution 4) If a system begins in the state loo〉-W,%), calculate and then plot the probability for the system to be in the initial state...
Let T: V V and S: V V and R: V V be three linear operators on V. Suppose we have T S= S R , Then prove ker(S) is an invariant subspace for R . We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Consider randomly selecting a student at U of T, and let denote the event that the selected student has a Visa credit card and be the analogous event for a Master Card. Suppose that , and . c) What is the probability of the event that the selected student has a Visa Card but does not have a Master Card? We were unable to transcribe this imageWe were unable to transcribe this imageP(A) 0.5 P(B) = 0.4 P(A n B)...
The behavior of a spin- particle in a uniform magnetic field in the z-direction, , with the Hamiltonian You found that the expectation value of the spin vector undergoes Larmor precession about the z axis. In this sense, we can view it as an analogue to a rotating coin, choosing the eigenstate with eigenvalue to represent heads and the eigenstate with eigenvalue to represent tails. Under time-evolution in the magnetic field, these eigenstates will “rotate” between each other. (a) Suppose...
a. Suppose that we have the state l) 2-1/2 (1010)1100)). How many (and which) particles are b. Suppose instead that we have the state l) 212(l000) |111). How many (and which) c. Suppose you measure the first particle from part (b) in the |0), |1) basis. What are the possible entangled? Explain why. particles are entangled? Explain why outcomes and their probabilities? On average, how many particles are entangled after the เงื่ measurement? a. Suppose that we have the state...
Quantum mechanics Consider a two-dimensional harmonic oscillator . If find the energy of the base state until second order in theory of disturbances and the energies of the first level excited to first order in . We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image