Question

What would be the result of a kinetic energy measurement on a free quantum particle? (i.e....

What would be the result of a kinetic energy measurement on a free quantum particle?

(i.e. potential energy V(x) = 0) of mass m with a wave-function ψ(x) = e^(-x^2)

A hint for this question:

Consider only the kinetic energy operator. Is the given function an eigenfunction of this operator?

If yes, what will be the result of the measurement?

If not an eigenfunction, what would be the result of the measurement?

0 0
Add a comment Improve this question Transcribed image text
Answer #1

Sol! To Find kinetic energy (K. E) on a free quantum particle. Givena potential Energy V(n)=0 of mass in A wave function 460)

Add a comment
Know the answer?
Add Answer to:
What would be the result of a kinetic energy measurement on a free quantum particle? (i.e....
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • Problem 4. Imagine you are a biophysical chemist and are interested in electron transport by membrane...

    Problem 4. Imagine you are a biophysical chemist and are interested in electron transport by membrane proteins. Let us consider the following wave function: (The above wave function corresponds to a free particle for which the potential energy V= 0) (a) Is the above wave function an eigenfunction of the momentum operator p? (b) Is the above wave function an eigenfunction of the operator for the momentum squared p2 ? (c) If your answer to part (b) is yes, then...

  • Free quantum particle. In Quantum Mechanics, is the time-independent Schrodinger's equation for a free particle in...

    Free quantum particle. In Quantum Mechanics, is the time-independent Schrodinger's equation for a free particle in one dimension. In this equation. is the wavefnnction of the particle, m is its mass. E is its (kinetic) energy, while is the fundamental Planck constant.

  • Question 21 Consider a free electron in one dimension (i.e. an electron free to move along...

    Question 21 Consider a free electron in one dimension (i.e. an electron free to move along say the x-direction on (a) The time-independent Schrödinger equation is Αψη (x)-Εηψη (x), where is the Hamiltonian (total energy) operator, and ψη (x) are the electron wave functions associated with energies En Assuming the electron's energy entirely comprises kinetic energy (as it is 'free' there is no potential energy term), write down the Schrödinger equation given that the momentum operator in one- dimension is...

  • 5. The relativistic corrections to the energy of a particle can be estimated by applying a...

    5. The relativistic corrections to the energy of a particle can be estimated by applying a fictitious "external potential” V = -p4/8m'c>, where p is the momentum of the particle, m is its mass, and c is the ħ d speed of light. Replacing p with its operator (p= ), the corresponding operator for the "external potential" is = - a . Is the ground state wavefunction of the particle in a box ( sin (**)) an eigenfunction of the...

  • QM 30 Relating classical and quantum mechanics IV. Supplement: Highly-excited energy eigenstates A particle is in...

    QM 30 Relating classical and quantum mechanics IV. Supplement: Highly-excited energy eigenstates A particle is in the potential well shown at right A. First, treat this problem from a purely elassical standpoint (assume the particle has enough energy to reach both regions) Give an example of a real physical situation that corresponds to this potential well. 1. region I | region II 2. In which region of the well would the particle have greater kinetic energy? Explain. 3. In which...

  • Write a functional programme in Python for the following task:   Consider the quantum mechanical problem of...

    Write a functional programme in Python for the following task:   Consider the quantum mechanical problem of a particle encountering a potential step of height V. The particle with wave number enters from the left and meets the potential step at 0. If the kinetic energy Eof the particle is larger than V, it can either pass the step and continue with a smaller wave number or be reflected keeping its kinetic energy. The formulae for the probability of transmission (T)...

  • In class we considered quantum tunneling of a particle of energy Eo through a barrier of...

    In class we considered quantum tunneling of a particle of energy Eo through a barrier of potential Vofor Vo > Eo. Here we focus on two aspects of the problem we ignored in class. In order to simplify we will only consider the initial first half of the barrier as shown below RegionI xS0 Regionx 20 Il There are two cases to consider: Eo< Vo Considered in class E>Vo Not considered in class Here we will focus on the second...

  • (III) Quantum Tunneling Consider an electron in 1D in presence of a potential barrier of width...

    (III) Quantum Tunneling Consider an electron in 1D in presence of a potential barrier of width L represented by a step function ſo I<0 or 1>L V U. r>0 and 2<L The total wavefunction is subject to the time-independent Schrödinger equation = EV (2) 2m ar2 +V where E is the energy of the quantum particle in question and m is the mass of the quantum particle. A The total wavefunction of a free particle that enters the barrier from...

  • QUESTION 1: In quantum mechanics, the behaviour of a quantum particle (like an electron, for example)...

    QUESTION 1: In quantum mechanics, the behaviour of a quantum particle (like an electron, for example) is described by the Schrödinger equation. The time-independent Schrödinger equation can be written in operator notation as H{y(x, y, z))-Ey(x, y, z) where H is known as the Hamiltonian operator and is defined as h2 2m Here, is a positive physical) constant known as Planck's constant and m is the mass of the particle (also Just a constant). V(x,y,Z) is a real-valued function. The...

  • Given the formula of the kinetic energy of a particle m with speed v: KE =...

    Given the formula of the kinetic energy of a particle m with speed v: KE = 1⁄2mv2 , and the formula of the gravitational potential energy: PE = -GMEm/R, where G is gravitational constant and ME and R=6378 km are the mass and the radius of Earth. Now the particle is shot from Earth surface to space. Find the minimum required initial speed for this particle to completely escape the influence of Earth gravity (i.e. PE=0). Notice that the gravitational...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT