Quantum Mechanic/wave function/junction condition

In summary, the conversation discusses how to eliminate C and D and obtain the last two equations, with a question about possible skipping of steps between the 4th and 5th equations. The speaker suggests either trusting the author or checking the algebra oneself, or a combination of both. They also recommend providing essential context for readers to understand the boundary conditions and wave numbers involved.
  • #1
GreenTea09
14
0
Junction Condition.jpg

May i know how do i eliminate C and D and how do i obtain the last two equations? Are there skipping of steps in between 4th to 5th equation? What are the intermediate steps that i should take to transit from 4th equation to the 5th equation?
 
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  • #2
It looks like quite a few steps have been skipped. You either trust the author or check the algebra yourself.
 
  • #3
Or the best of both worlds: trust, but verify. Doing a messy calculation is like eating oatmeal, not pleasant in the moment but makes things easier later.
 
  • #4
And for the sake of PF readers: provide essential context so we can see where these boundary condition equations are sitting ! And where the wave number is ##k_i, k_i', k_i''## (hey, can we skip the subscript 1 ?
 

1. What is quantum mechanics?

Quantum mechanics is the branch of physics that deals with the behavior of matter and energy at a very small scale, such as atoms and subatomic particles. It describes how these particles behave and interact with each other.

2. What is a wave function?

A wave function is a mathematical function that describes the quantum state of a particle. It contains information about the probability of finding the particle in a particular location or state.

3. What is the junction condition in quantum mechanics?

The junction condition, also known as the boundary condition, is a rule that determines how the wave function of a particle changes when it encounters a boundary or obstacle. It helps to predict how the particle will behave in different environments.

4. How does quantum mechanics differ from classical mechanics?

Classical mechanics describes the behavior of larger objects, while quantum mechanics deals with the behavior of particles at a very small scale. In classical mechanics, objects have definite positions and velocities, while in quantum mechanics, particles have a probability of being in multiple positions or states at once.

5. What is the significance of quantum mechanics in modern science?

Quantum mechanics is essential for understanding many phenomena in modern science, such as the behavior of atoms, molecules, and subatomic particles. It also plays a crucial role in technologies such as transistors, lasers, and computer memory.

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