Time Independent Schrodinger Equation Question

In summary, the one-dimensional time-independent Schrodinger equation for a particle of mass m and total energy E in a potential V(x) is stated. For an infinite square potential well with V(x) = 0 for 0 < x < l and V(x) = infinite for all other x, the problem of finding a general solution for the wavefunction is discussed. The potential conditions at x = 0 and x = l are used as boundary conditions to determine the coefficients of the general solution in the region where V(x) = 0.
  • #1
Physicist_FTW
9
0
1. State the one dimensional time - INdependant Schrodinger equation for a particle of mass m and total energy E in a potential V(x). For an infinite square potential well V(x)=0
(0<x<l) and V(x) = infinite (all other x) find a general solutionfor the wavefunction of this function of this particle.



2. Time Independant Schrodinger equation



3. I know what the Schrondinger equation is so stateing that is no probelm, also for V(x) equal to 0 i can get a value however as for a general solution I am kinda stuck could someone help?
 
Physics news on Phys.org
  • #2
This is the classic "particle in a box" problem (i'm sure you could actually just find the solution by wiki'ing it), however, let me offer some hints. By saying that V(x) = infinity at x>l and x<0 it is basically saying that your solution for the V(x)=0 region has to vanish at x=l and x=0 (i.e.) psi(l)=0 and psi(0)=0. This basically juts gives you two boundary conditions through which to determine the coefficients of the general solution found in the V(x)=0 region. Hope that helps
 

1. What is the Time Independent Schrodinger Equation?

The Time Independent Schrodinger Equation is a fundamental equation in quantum mechanics that describes the behavior of a non-relativistic particle moving in a potential field. It is used to calculate the wave function of a particle, which gives information about the probability of finding the particle at a certain location and time.

2. What does the Time Independent Schrodinger Equation tell us about a particle?

The Time Independent Schrodinger Equation tells us about the energy levels and corresponding wave functions of a particle in a given potential. It also gives us information about the probability of finding the particle at a certain energy level and location.

3. How is the Time Independent Schrodinger Equation derived?

The Time Independent Schrodinger Equation is derived from the more general Schrodinger Equation, which describes the time evolution of a quantum system. By assuming that the system is time independent, the time-dependent term in the Schrodinger Equation cancels out, resulting in the simplified Time Independent Schrodinger Equation.

4. What are the applications of the Time Independent Schrodinger Equation?

The Time Independent Schrodinger Equation has many applications in quantum mechanics, including calculating the energy levels and wave functions of particles in potential fields, determining the probability of finding a particle in a certain state, and predicting the behavior of quantum systems.

5. How does the Time Independent Schrodinger Equation relate to the Uncertainty Principle?

The Time Independent Schrodinger Equation is a key component in understanding the Uncertainty Principle, which states that it is impossible to know both the position and momentum of a particle with absolute certainty. The Time Independent Schrodinger Equation gives us information about the probability of finding a particle at a certain location, but it cannot determine the exact position of the particle. This is related to the Uncertainty Principle, as the more precisely we know the position of a particle, the less we know about its momentum, and vice versa.

Similar threads

  • Advanced Physics Homework Help
Replies
5
Views
980
  • Advanced Physics Homework Help
Replies
5
Views
1K
  • Advanced Physics Homework Help
Replies
4
Views
1K
  • Advanced Physics Homework Help
Replies
9
Views
1K
  • Advanced Physics Homework Help
Replies
2
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
907
Replies
2
Views
1K
  • Advanced Physics Homework Help
Replies
10
Views
428
Replies
3
Views
1K
Back
Top