Consider a simple harmonic oscillator in one dimension. Do the following algebraically, that is,without using wavefunctions.a) Construct a linear combination of |0) and |1) such that the expected position (x) is as large aspossibleb) Suppose the oscillator is in the state you found in part (a) at time t -vector for t> 0 in the Schrödinger picture? Evaluate the expectation value (x) at time t using (i)the Schrödinger picture and (ii) the Heisenberg picture.0. What is the statec) Evaluate the uncertainty in position, ((Ax)) as a function of time using either picture.

Question
Asked Nov 20, 2019
83 views

It's a quantum mechanics question.

Consider a simple harmonic oscillator in one dimension. Do the following algebraically, that is,
without using wavefunctions.
a) Construct a linear combination of |0) and |1) such that the expected position (x) is as large as
possible
b) Suppose the oscillator is in the state you found in part (a) at time t -
vector for t> 0 in the Schrödinger picture? Evaluate the expectation value (x) at time t using (i)
the Schrödinger picture and (ii) the Heisenberg picture.
0. What is the state
c) Evaluate the uncertainty in position, ((Ax)) as a function of time using either picture.
help_outline

Image Transcriptionclose

Consider a simple harmonic oscillator in one dimension. Do the following algebraically, that is, without using wavefunctions. a) Construct a linear combination of |0) and |1) such that the expected position (x) is as large as possible b) Suppose the oscillator is in the state you found in part (a) at time t - vector for t> 0 in the Schrödinger picture? Evaluate the expectation value (x) at time t using (i) the Schrödinger picture and (ii) the Heisenberg picture. 0. What is the state c) Evaluate the uncertainty in position, ((Ax)) as a function of time using either picture.

fullscreen
check_circle

Expert Answer

star
star
star
star
star
1 Rating
Step 1

(a)

The linear combination of the wave function can be written as,

help_outline

Image Transcriptionclose

)C0)+1) =

fullscreen
Step 2

The large expectation value of x can be determined as,

help_outline

Image Transcriptionclose

h (a+a' w) (vx\v)= V2ma h (01+G (1|(a + a' )e, |0)+G|1) 2ma h (G'c, +c,'c) C 2mo

fullscreen
Step 3

To maximize the expec...

help_outline

Image Transcriptionclose

lesf +le°= cos0 and c = sin 0 Let c, 1 and c . Co

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Science

Advanced Physics

Related Advanced Physics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: a) 95 μm  b) 90 μm c) 85 μm  d) 80 μm

A: The intensity of the neutron beam is

question_answer

Q: Using Dirac delta functions in the appropriate coordinate system, express the following charge distr...

A: a) Consider the charge distribution given by,

question_answer

Q: A turbocharged aircraft engine cylinder has a total volume of 80 cu. in. and a clearance volume of 1...

A: Given that ,Total Volume = Volume of the cylinder before compression V1 = Vs + Vc = 80 in3Clearance ...

question_answer

Q: Locate the radial distance of the radial nodes in the 3s orbital of an H atom.a.) node closest to nu...

A: The expression for the radial wave function of a 3s orbital of a hydrogen atom is given by,

question_answer

Q: What is a boson? Is a gluon the same thing? How do they work? What makes up electrons?

A: The following Standard model table differentiates between the Bosons and the Fermions on the basis o...

question_answer

Q: It's a quantum mechanics problem.

A: The Hamiltonian of the particle is given by

question_answer

Q: When asked for the altitude for the moon would I use arc degrees to measure that?

A: the altitude of the moon is measured from the horizon to the point where the center of the moon exis...

question_answer

Q: Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel...

A: (a) Write an expression for final angular velocity

question_answer

Q: State the total number of quantum states available to an electron in the levels in a hydrogen atom t...

A: In the above problem it is assumed that the expression for the energy of an electron in a hydrogen a...