Expectation Value of Energy for Nonstationary State in Infinite Square Well

  • Thread starter KHU2
  • Start date
  • Tags
    States
In summary, the conversation discusses the behavior of a particle in an infinite square well of width L, initially described by a wavefunction that is a superposition of the ground and first excited states. The first two tasks are to find the value of C for normalization and the wave function at any later time. The last task is to demonstrate that the expectation value of the energy in this state is equal to the average of the energies of the first two stationary states.
  • #1
KHU2
1
0
8)
Consider a particle in an infinite square well of width L. Initially, (at t=0) the system is
described by a wavefunction that is equal parts a superposition of the ground and first
excited states:
Ψ(x, 0)=C[Ψ1(x)+Ψ2(x)]
a) Find C so that the wavefunction is normalized
b) Find the wave function at any later time t.
c)show that the expectation value of the energy in this state is (E1+E2)/2, where E1 AND E2 ARE THE ENERGIES OF THE FIRST TWO STATIONARY STATES.


I DID a) and b) , i don't how to do c) , could you help me
 
Physics news on Phys.org
  • #2
So, if [tex]\psi(x,t)[/tex] is your wavefunction, what is the expectation value of the Hamiltonian operator?
 
  • #3
p.s. you may just do it at t=0, but don't forget to prove that you *can*.
 

FAQ: Expectation Value of Energy for Nonstationary State in Infinite Square Well

What are nonstationary states?

Nonstationary states, also known as time-dependent states, are quantum states that change over time and do not have a constant probability distribution. This means that the probability of finding a particle in a nonstationary state at a particular location changes over time.

How do nonstationary states differ from stationary states?

Stationary states, also known as time-independent states, are quantum states that do not change over time and have a constant probability distribution. This means that the probability of finding a particle in a stationary state at a particular location does not change over time.

What causes a system to be in a nonstationary state?

A system can be in a nonstationary state due to a variety of factors, such as an external force or perturbation acting on the system, or the system undergoing a change in energy level. In quantum mechanics, particles can also transition between stationary and nonstationary states through a process known as quantum tunneling.

How are nonstationary states represented in quantum mechanics?

In quantum mechanics, nonstationary states are represented using time-dependent wave functions, which describe the probability amplitude of finding a particle in a nonstationary state at a particular location and time. These wave functions are solutions to the time-dependent Schrödinger equation.

What are some applications of nonstationary states?

Nonstationary states have a variety of applications in quantum mechanics, particularly in fields such as quantum computing and quantum cryptography. They also play a crucial role in understanding the behavior of particles in systems that are subject to external forces or fluctuations, such as in chemical reactions or nuclear decay processes.

Similar threads

Minimum time between two orthogonal states
Replies
2
Views
1K
Stationary states infinite cubic well
Replies
3
Views
1K
Average value of the impulse as the parameters vary
Replies
14
Views
2K
Most Probable energy after infinite square well expands
Replies
2
Views
766
Triggering a Transition Between Quantum States
Replies
1
Views
2K
Energy Uncertainty and expectation value of H
Replies
2
Views
2K
Expectation Values <E> and <E^2>
Replies
6
Views
3K
Is the given wave function a stationary state?
Replies
3
Views
2K
What are the expectation values for position and momentum in states Ψ0 and Ψ1?
Replies
3
Views
2K
Infinite Square Well homework problem
Replies
18
Views
2K

Hot Threads

Recent Insights

Back
Top