calculate the expectation values of x, x2, p, p2 in n = 0 to n =...

calculate the expectation values of x, x2, p, p2 in n = 0 to n = 10 states in HARMONIC OSCILLATOR. (DO NOT USE LADDER OPERATOR METHOD).

solve it by considering harmonic oscillator WAVEFUNCTION

Expert Solution

genius_generous answered 3 hours ago

Calculate the expectation values of p and p2 for a particle in the state n =...

Calculate the expectation values of p and p2 for a particle in the state n = 2 in a square-well potential. Hint: You can do it by straight forward substitution of the appropriate y and A in calculating <A> = <y|A|y> or you can use some ingenuity to get the aswer.

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.

Given a difference equation x[n+2] + 5x[n+1]+6x[n]=n with start values x[0]= 0 and x[1]=0

Using the inner product on 〈p, q〉 = ∫(0 to1) p(x)q(x)dx on P2, write v as the...

Using the inner product on 〈p, q〉 = ∫(0 to1) p(x)q(x)dx on P2, write v as the sum of a vector in U and a vector in U⊥, where v=x^2, U =span{x+1,9x−5}.

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).

Using the normal distribution, calculate the following probabilities: a) P(X≤16|n=50, p=0.70) b) P(10≤X≤16|n=50, p=0.50)

Suppose that random variable X 0 = (X1, X2) is such that E[X 0 ] =...

Suppose that random variable X 0 = (X1, X2) is such that E[X 0 ] = (µ1, µ2) and var[X] = σ11 σ12 σ12 σ22 . (a matrix) (i) Let Y = a + bX1 + cX2. Obtain an expression for the mean and variance of Y . (ii) Let Y = a + BX where a' = (a1, a2) B = b11 b12 0 b22 (a matrix). Obtain an expression for the mean and variance of Y . (ii)...

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

Sketchthegraphofthefunctiony=20x−x2 from x=0 to x=20. • Next, with five equal intervals (i.e. with n = 5),...

Sketchthegraphofthefunctiony=20x−x2 from x=0 to x=20. • Next, with five equal intervals (i.e. with n = 5), compute the trape- zoidal, T , and Simpson’s rule S, estimates for the following integral J= integral 0 to 20 (20x−x^2)dx. • Finally compute the exact value of the integral J . • Compare the exact value with the your estimates T and S and discuss.

For the diﬀerential equation x′′ + (o.1)(1 − x2)x′ + x = 0; x(0) = 1,...

For the diﬀerential equation x′′ + (o.1)(1 − x2)x′ + x = 0; x(0) = 1, x′(0) = 0. (a) Rewrite it as a system of ﬁrst order diﬀerential equations in preparation to solve with the vectorized version of a numerical approximation technique. (b) Use the vectorized Euler method with h = 0.2 to plot out an approximate solution for t = 0 to t = 10. (c) Plot the points to the approximated solution (make a scatter plot), make...

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