JCP321H5 Lecture Notes - Lecture 4: Matter Wave, Copenhagen Interpretation, Agnosticism
The Schrodinger Equation
Relevance
What is it?
The fundamental equation for the
behaviour of a quantum mechanical
system
How does it work?
Here is the 1D Schrodinger equation:
If we were to solve it, the solution
would be this
If we messed around with this a little
using the definition of the Hamiltonian
above, we would then get this:
In three dimensions, the Schrodinger
equation looks like this:
And it's solutions are applicable to the
concept of electron orbitals.
What is it used for?
The “particle in a box”
Even though it's an idealized case, it's
very good for showing how the results
of this equation result in quantized
energy levels
The main use of the Schrodinger
equation is to mathematically describe
quantized energy levels (think orbitals
of an electron)
Why is it important?
The Schrodinger equation is to
quantum mechanics as Newton’s laws
of motion are to classical mechanics.
Wave function
Relevance
What is it?
a mathematical description of the
quantum state of an isolated system
How does it work?
Below is an visualization of what the
wave function looks like:
The main use for the wave function is
for finding the probability that a matter
wave (like an electron) will be located
in any given region of space:
The square of the wave function is a
probability distribution:
Document Summary
The fundamental equation for the behaviour of a quantum mechanical system. If we were to solve it, the solution would be this. If we messed around with this a little using the definition of the hamiltonian above, we would then get this: In three dimensions, the schrodinger equation looks like this: And it"s solutions are applicable to the concept of electron orbitals. Even though it"s an idealized case, it"s very good for showing how the results of this equation result in quantized energy levels. The main use of the schrodinger equation is to mathematically describe quantized energy levels (think orbitals of an electron) The schrodinger equation is to quantum mechanics as newton"s laws of motion are to classical mechanics. Relevance a mathematical description of the quantum state of an isolated system. Below is an visualization of what the wave function looks like:
