Answered: 20. In Sec. 3.7, the standard deviation… | bartleby

Related questions

Question

20. In Sec. 3.7, the standard deviation o of a set of N measure-
ments of some quantity x was defined as [A + CO1
i=1
(a) Show that, in terms of expectation values, this formula
can be written as
=
%3D
(b) If the uncertainty in position of a particle in a box is
taken as the standard deviation, find the uncertainty in
the expectation value (x) = L/2 for n = 1. (c) What is the
limit of Ax asn increases?

Expert Solution

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Solve the following.
What is the approximate transmission probability (in %) of an electron with total energy 1.3 eV through a barrier of thickness 586 pm, and a potential height of 2.367 eV? (Does it matter what the potential energy is before and after the barrier? Not for this approximation, as long as it is <1.3 eV, so in both cases there is a travelling wave.)
7.
It's a quantum mechanics question.
2. A simple harmonic oscillator is in the state 4 = N(Yo + λ 4₁) where λ is a real parameter, and to and ₁ are the first two orthonormal stationary states. (a) Determine the normalization constant N in terms of λ. (b) Using raising and lowering operators (see Griffiths 2.69), calculate the uncertainty Ax in terms of .
An electron with an initial kinetic energy of 1.542 eV (in a region with 1.095 eV potential energy) is incident on a potential step (extending from x=0 to ∞) to V=2.381 eV. What is the transmission probability (in %)? FYI: If we had a travelling wave arriving at a similar potential DROP, then k1 (for x<0) would be real and the symmetry of R=(k1-k2)2/(k1+k2)2 implies reflection/transmission are the same as a potential RISE with the same energies but k1 and k2 swapped.
11. Evaluate (r), the expectation value of r for Y,s (assume that the operator f is defined as "multiply by coordinate r).Why does (r) not equal 0.529 for Y,,? In this problem,use 4ardr = dt.
Please don't provide handwritten solution ..... Determine the normalization constant for the wavefunction for a 3-dimensional box (3 separate infinite 1-dimensional wells) of lengths a (x direction), b (y direction), and c (z direction).
3.7 Suppose that a wave function (r,t) is normalized. Show that the wave function e¹0 W(r,t), where 0 is an arbitrary real number, is also normalized.