Question

Consider the ground state of the harmonic oscillator.

(a) (7 pts) Calculate the expectation values <x>, <x2>, <p> and <p2>.

(b) (3 ps) What is the product ΔxΔp, where the two quantities are standard deviations? (This is easy if you did part (a)). How does this answer compare with the prediction of the Uncertainty Principle?

Answer #1

For a harmonic oscillator in the ground-state,
determine △p and △x. How does the value of △p△x compare to the
Heisenberg Uncertainty Principle?

Q. 2(a) For the first excited state of harmonic oscillator,
calculate <x>, <p>, <x2>, and <p2>
explicitly by spatial integration. (b) Check that the
uncertainty principle is obeyed.
(c) Compute <T> and <V>. .

The ground state of a particle is given by the time‐dependent
wave function
Ψ0(x, t) =
Aeαx^2+iβt
with an energy eigenvalue of E0 =
ħ2α/m
a. Determine the potential in which this particle exists. Does this
potential resemble any that you have seen before?
b. Determine the normalization constant A for this wave
function.
c. Determine the expectation values of x,
x2, p, and
p2.
d. Check the uncertainty principle Δx and Δp. Is
their product consistent with the uncertainty...

For a particle in the first excited state of harmonic oscillator
potential,
a) Calculate 〈?〉1, 〈?〉1, 〈? 2〉1, 〈? 2〉1.
b) Calculate (∆?)1 and (∆?)1.
c) Check the uncertainty principle for this state.
d) Estimate the length of the interval about x=0 which
corresponds to the classically allowed domain for the first excited
state of harmonic oscillator.
e) Using the result of part (d), show that position uncertainty
you get in part (b) is comparable to the classical range of...

Quantum mechanics:
Consider a particle initially in the ground state of the
one-dimensional simple harmonic oscillator. A uniform electric
field is abruptly turned on for a time t and then abruptly turned
off again. What is the probability of transition to the first
excited state?

1. For a pair of sample x- and y-values, what is the difference
between the observed value of y and the predicted value of y? a) An
outlier b) The explanatory variable c) A residual d) The response
variable
2. Which of the following statements is false:
a) The correlation coefficient is unitless. b) A correlation
coefficient of 0.62 suggests a stronger correlation than a
correlation coefficient of -0.82. c) The correlation coefficient,
r, is always between -1 and 1....

1) Describe an example of each of the following that may be
found of your kitchen: Explain how your choice falls into this
category, and if there is a chemical name or symbol for it, provide
that as well. Provide a photo of your example with your ID card in
it. a) a compound b) a heterogeneous mixture c) an element (symbol)
Moving to the Caves… Lechuguilla Caves specifically. Check out this
picture of crystals of gypsum left behind in...

2. SECURING THE WORKFORCE Diversity management in
X-tech, a Japanese organisation
This case is intended to be used as a basis for class discussion
rather than as an illustration of the effective or ineffective
handling of an administrative situation. The name of the company is
disguised.
INTRODUCTION
In light of demographic concerns, in 2012, the Japanese
government initiated an effort to change the work environment in
order to secure the workforce of the future. Japan is world
renowned for its...

3 SECURING THE WORKFORCE Diversity management in X-tech,
a Japanese organisation
This case is intended to be used as a basis for class discussion
rather than as an illustration of the effective or ineffective
handling of an administrative situation. The name of the company is
disguised.
INTRODUCTION
In light of demographic concerns, in 2012, the Japanese
government initiated an effort to change the work environment in
order to secure the workforce of the future. Japan is world
renowned for its...

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INNOVATION
Deep Change: How Operational Innovation Can Transform Your
Company
by
Michael Hammer
From the April 2004 Issue
Save
Share
8.95
In 1991, Progressive Insurance, an automobile insurer based in
Mayfield Village, Ohio, had approximately $1.3 billion in sales. By
2002, that figure had grown to $9.5 billion. What fashionable
strategies did Progressive employ to achieve sevenfold growth in
just over a decade? Was it positioned in a high-growth industry?
Hardly. Auto insurance is a mature, 100-year-old industry...

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