1. Determine the variance in position and momentum, Δx2=<x2>−<x>2 and Δp2=<p2>−<p>2 for the ground-state SHO and...

1. Determine the variance in position and momentum, Δx²=<x²>−<x>² and Δp²=<p²>−<p>² for the ground-state SHO and show that they satisfy the Heisenberg uncertainty relation, (Δx)(Δp)≥ℏ2

Expert Solution

genius_generous answered 4 months ago

Compute the average of x and x^2 and determine ∆x for the ground state of the...

Compute the average of x and x^2 and determine ∆x for the ground state of the harmonic oscillator. b) Determine the average potential energy and describe how it is related to the total energy?

Let p0 = 1+x; p1 = 1+3x+x2; p2 = 2x+x2; p3 = 1+x+x2 2 R[x]. (a)...

Let p0 = 1+x; p1 = 1+3x+x2; p2 = 2x+x2; p3 = 1+x+x2 2 R[x]. (a) Show that fp0; p1; p2; p3g spans the vector space P2(R). (b) Reduce the set fp0; p1; p2; p3g to a basis of P2(R).

particle in a well 1. Using the uncertainty principle for position and momentum, estimate the ground...

particle in a well 1. Using the uncertainty principle for position and momentum, estimate the ground state energy for an infinite well of width a, compare the obtained result with the one found in the lecture. 2. Compute <p> and <x> for the particle in a box. 3. Prove that the eigenfunctions ψn(x) are orthogonal . 4. What are the energies of the ground state, first excited and second excited states for an electron trapped in an infinite well of...

Calculate the variance of random variable X if P(X = a) = p= 1 -P(X =...

Calculate the variance of random variable X if P(X = a) = p= 1 -P(X = b).

Consider the linear transformation T : P2 ? P2 given by T(p(x)) = p(0) + p(1)...

Consider the linear transformation T : P2 ? P2 given by T(p(x)) = p(0) + p(1) + p 0 (x) + 3x 2p 00(x). Let B be the basis {1, x, x2} for P2. (a) Find the matrix A for T with respect to the basis B. (b) Find the eigenvalues of A, and a basis for R 3 consisting of eigenvectors of A. (c) Find a basis for P2 consisting of eigenvectors for T.

For the following probability mass function, p(x)=1/x for x=2, 4, 8 p(x) = k/x2 for x=16...

For the following probability mass function, p(x)=1/x for x=2, 4, 8 p(x) = k/x2 for x=16 Find the value of k. Find the standard deviation of (7-9X).

2a. Confirm that the position and momentum, p=-ℏ ∂/∂x, operators do not commute. 2b. Show how...

2a. Confirm that the position and momentum, p=-ℏ ∂/∂x, operators do not commute. 2b. Show how the statement above limits the ability for a state that to be both an eigenstate of position and momentum concurrently. 2c. For an eigenstate where the momentum is zero, show that x than p leads to a result, xp, that is different than that of p then x.

2. For the function : f(x) = x2 − 30x − 2 a) State where f...

2. For the function : f(x) = x2 − 30x − 2 a) State where f is increasing and where f is decreasing b) Identify any local maximum or local minimum values. c) Describe where f is concave up or concave down d) Identify any points of inflection (in coordinate form) 3. For the function f (x)= x4 − 50 2 a) Find the intervals where f is increasing and where f is decreasing. b) Find any local extrema and...

k1 = k2 m1=9m^2 P1=P2 What is the relationship between P1 and P2? The momentum will...

k1 = k2 m1=9m^2 P1=P2 What is the relationship between P1 and P2? The momentum will be the same? K represents kinetic energy

sin(tan-1 x), where |x| < 1, is equal to: (a) x/√(1 – x2) (b) 1/√(1 – x2) (c) 1/√(1 + x2) (d) x/√(1 + x2)

sin(tan-1 x), where |x| < 1, is equal to:(a) x/√(1 – x²)(b) 1/√(1 – x²)(c) 1/√(1 + x²)(d) x/√(1 + x²)

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