Shrodinger equation/Particle in a box

  • Thread starter Linus Pauling
  • Start date
  • Tags
    Box
In summary, the conversation discusses the function U(x)psin(x) in the interval 0 < x < L and its relationship to the second derivative of psi(x). The incorrect answer is obtained when U(x) is added to the second derivative of psi multiplied by -h-bar/2m. Clarifying the problem and using latex may help in receiving assistance.
  • #1
Linus Pauling
190
0
1. What is U(x)psin(x) in the interval 0 < x < L? (less than or equal to)



2. In previous problems I had found the following:

Second deriv. of psi(x) = -(n*pi/L)2*C*sin(n*pi*x/L)

U(x)*psin(x) = 0





3. From the above and the Shrodinger equation, I added U(x) = 0 to the second derivative of psi given above multiplied by -h-bar/2m, obtaining the incorrect answer of:

(h-bar*n*pi)2/2mL2 * C * sin(n*pi*x/L)
 
Physics news on Phys.org
  • #2
I don't think you will receive much help if you don't clearly explain your problem. For example, what is U(x)? Also, you might want to use latex or people will be put off trying to decipher what you wrote.
 

FAQ: Shrodinger equation/Particle in a box

What is the Schrodinger equation?

The Schrodinger equation is a mathematical equation that describes the behavior of quantum particles, such as electrons, in a given system. It was developed by Austrian physicist Erwin Schrodinger in 1926 and is a fundamental equation in quantum mechanics.

What is the significance of the particle in a box model?

The particle in a box model is a simplified version of the Schrodinger equation that helps us understand the behavior of quantum particles in a confined space. It is often used as an introductory example in quantum mechanics and is useful for understanding concepts such as energy quantization and wave-particle duality.

How does the Schrodinger equation relate to the uncertainty principle?

The Schrodinger equation incorporates the uncertainty principle, which states that it is impossible to know both the position and momentum of a particle with absolute certainty. The equation describes the probability of finding a particle in a certain position, rather than its exact location, reflecting the uncertainty inherent in quantum systems.

Can the Schrodinger equation be solved analytically?

In most cases, the Schrodinger equation cannot be solved analytically, meaning there is no exact mathematical solution. Instead, it is typically solved numerically using computational methods. However, there are a few simple systems, such as the particle in a box, for which analytical solutions can be found.

What are the applications of the Schrodinger equation?

The Schrodinger equation is used in a wide range of applications, including quantum chemistry, solid state physics, and electronics. It is essential for understanding the behavior of atoms, molecules, and materials at the quantum level, and has also played a crucial role in the development of technologies such as transistors and lasers.

Similar threads

Help Calculating probability between 2 limits for the ground state
Replies
28
Views
1K
Energy of particle in simple harmonic motion
Replies
13
Views
273
Particle in a box : Schrodinger Eq
Replies
5
Views
2K
A relativistic electron in a potential box
Replies
4
Views
1K
Graphing the Superposition of Two Standing Waves
Replies
8
Views
1K
Equivalence of Euler-Lagrange equations and Cardinal Equations for a rigid planar system
Replies
4
Views
547
Fourier series, periodic function for a string free at each end
Replies
8
Views
1K
Number of Different resonances in a closed Box
Replies
6
Views
2K
1D Particle & Energy w/ F(x): Am I doing this right?
Replies
7
Views
1K
How Do You Normalize the Wave Function for a Particle in an Infinite Well?
Replies
14
Views
1K

Hot Threads

Recent Insights

Back
Top