Quantum Mechanics question

In summary, the potential function V(x)={Inf for x<0, bx for 0<x<a, Inf for x>a} differs from V(x)={Inf for x<0, bx for x>0} in terms of Schrodinger's equation, wave functions, and energy states. Treating an infinite potential within the context of 1-dim SE requires a substitution in the equation and solving a differential equation. The concept of infinite potential specifies a boundary condition for the DE.
  • #1
18
0
How does this potential:

V(x)={Inf for x<0, bx for 0<x<a, Inf for x>a}

differ from:

V(x)={Inf for x<0, bx for x>0}

with regards to Schrodinger's equation, wave functions, and the energy states.

P.S. the tex graphics are not showing when I try to post my question using tex macros. This is why I resorted to plain ascii.
 
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  • #2
Do you know how to treat an infinite potential within the context of 1-dim SE ?
 
  • #3
This is the part that I have trouble with. I know that if I had a constant
potential or any other type of potential, then a substitution in Schrodinger's
equation will be required. From there I will have to solve a DE. But in
the case of infinite potential I am not sure.
 
  • #4
Saying 'infinite potential' specifies a boundary condition for the DE. Guess which one?
 
  • #5
I think I got it. Thanks.
 

1. What is Quantum Mechanics?

Quantum Mechanics is a branch of physics that studies the behavior of particles at the atomic and subatomic level. It explains the principles of how these particles interact with each other and the laws that govern their behavior.

2. How does Quantum Mechanics differ from Classical Mechanics?

Classical Mechanics describes the behavior of larger objects, while Quantum Mechanics focuses on the behavior of particles at a very small scale. The laws of Classical Mechanics do not apply in the quantum world, and instead, a new set of laws and principles are needed to explain the behavior of particles at this level.

3. What are some real-life applications of Quantum Mechanics?

Quantum Mechanics has numerous practical applications, including the development of new technologies such as transistors, lasers, and superconductors. It also plays a crucial role in the fields of chemistry, biology, and materials science.

4. What is the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle states that it is impossible to know the exact position and momentum of a particle at the same time. This means that the more accurately we know the position of a particle, the less we know about its momentum, and vice versa.

5. How does Quantum Mechanics explain the concept of entanglement?

Entanglement is a phenomenon in which two particles become connected in such a way that the state of one particle directly affects the state of the other, no matter how far apart they are. Quantum Mechanics explains this as a result of the particles being described by a single wave function, and their states being linked despite any physical distance between them.

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