Can the Schrondinger Wave Equation Be Used to Solve Normalized Cases?

In summary, the conversation discusses the normalized case of solving the Schrodinger wave equation. The Schrodinger equation is a linear equation and when normalizing the solution, a constant is chosen such that the integral of the solution squared is equal to 1. The conversation also mentions using the infinite square well as a simple example for solving the normalized case. However, the poster also brings up the concept of finding momentum in the x and y direction, and asks for similar examples.
  • #1
vick5821
8
0

Homework Statement



Solving Normalized case of schrondinger wave equation

Homework Equations





The Attempt at a Solution



This type of question is not normalized case of solving using schrondiger equation. Any example of solving normalized case using schrondinger equation ? How would it be ? Using same formula and same way of solving ?

Thank you
 

Attachments

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  • #2
The Schrodinger equation is a linear equation, so if ##\psi## is a solution, any constant multiple of it will also be a solution. When normalize the solution, you're simply requiring that the constant be chosen such that
$$\int \psi^*\psi\,dx = 1.$$
 
  • #3
Yes. I am aware about that. Just that I wanted some example problem solving on how to solve for normalize case and how would the question asked ?

Thank you
 
  • #4
What do you mean by "solve for normalize case"? I suggest you look up the infinite square well in your textbook. That's probably the simplest example.
 
  • #5
As attached, the wave equation given is not normalized case and we solve it using Not Normalized method. I want to ask how would it be if the wave equation given is in NORMALISED form and how to solve it ?

Thank you
 
  • #6
What you're saying doesn't make sense. There is no such thing as a normalized case of the wave equation. You have the wave equation. You find solutions. You normalize the solutions. That's it.
 
  • #7
Initially, I get the wave equation , then I try to do see whether the wave equation is normalized or not by see this condition :
If
<refer attachment>

then the wave equation is normalized.

If it is not, means the wave equation is not NORMALIZED
 

Attachments

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  • #8
The (time-independent) wave equation is
$$-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}\psi + V(x)\psi = E\psi.$$ ##\psi## is a solution to the wave equation.

Take a look at http://physicspages.com/2011/01/26/the-infinite-square-well-particle-in-a-box/.
 
  • #9
Have you refer to the very first attachment ? It is given the solution of the wave equation already. But we have to find the momentum in x and y
 
  • #10
vela said:
The (time-independent) wave equation is
$$-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}\psi + V(x)\psi = E\psi.$$ ##\psi## is a solution to the wave equation.



Any similar question ?
 

1. What is the Schrödinger Wave Equation?

The Schrödinger Wave 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 Schrödinger in 1925 and is a fundamental concept in quantum mechanics.

2. What is the significance of the Schrödinger Wave Equation in physics?

The Schrödinger Wave Equation allows us to understand the behavior of quantum particles, which are the building blocks of matter. It helps us to predict the probability of finding a particle in a particular location and to understand the wave-like nature of particles.

3. How does the Schrödinger Wave Equation differ from classical physics equations?

The Schrödinger Wave Equation is a quantum mechanical equation that describes the behavior of particles at the subatomic level, while classical physics equations describe the behavior of larger objects. The Schrödinger Wave Equation takes into account the wave-like nature of particles and the uncertainty principle, which are not considered in classical physics equations.

4. Can the Schrödinger Wave Equation be solved exactly?

In most cases, the Schrödinger Wave Equation cannot be solved exactly. Instead, scientists use approximations and numerical methods to solve the equation and make predictions about the behavior of quantum particles. However, there are a few special cases where the equation can be solved exactly, such as the particle in a box or the harmonic oscillator.

5. How does the Schrödinger Wave Equation relate to the concept of superposition?

The Schrödinger Wave Equation allows us to describe the state of a particle as a combination of multiple possible states, known as the principle of superposition. This concept is essential in understanding quantum mechanics and is the basis for phenomena such as interference and entanglement.

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