[inspiration100]

Hey guys,

I'm taking the first quarter of physical chemitry and I feel like I'm missing the big picture here.  Here's where I get stuck:  I don't exactly understand the concept of eigenspace.  I understand that the wavefunction is generally an eigenfunction and the eignevalue of that eignefunction is the energy from the schrodinger equation.  So I feel I'm missing the link between the wavefunction and eigenspace.  How do the two relate?  What exactly is the meaning of the wavefunction, other than it can be used inside the schrodinger equation?

Some of these basics are holding me up in the class so I'm hoping someone can throw me down the basics in "simple" terms.

Thanks!

[Schrödinger]

A wavefunction is basically a function, which contains all the information about a particle. It is the operator you use on it and the operation you perform on it that defines the result that you get out of the operation.

For instance, Hamiltonian H is the operator that one uses to extract the value of energy from the wavefunction using the Schrödinger equation.

A simple and very crude analogy : Basically, it is like a telephone directory. Doing an address search gives the address results, a number search gives a number result and a name search gives a name result.

[inspiration100]

Thanks for the clean and simple response Erwin Schrodinger  !  So how does it apply to vectorspace?  In my pchem notes it says 'the space of all wavefunctions is a vectorspace" and he goes to write the following:

ψ(x) = Σ(i) Ci x Φi(x)
where Ci = ∫−∞ to ∞ (Φi*(x) * ψ(x)) d(x)

I don't understand what this is saying.  I presume Φ(x) must be an eigenfunction, but wouldn't C then be an eigenvalue of the eigenfunction?  Why does this equal the wavefunction?

Thanks for helping me out, you guys are going to save me in pchem!

[Jorriss]

Read about the following from a linear algebra textbook.

1) Vector Space
2) Basis
3) Representation of an abstract vector in a particular basis

Most wavefunctions are not eigenfunctions, generally speaking, a system is not in a state represented by an eigenfunction. But a system can be represented as a linear combination of eigenfunctions of a type.

[juanrga]

Hey guys,

I'm taking the first quarter of physical chemitry and I feel like I'm missing the big picture here.  Here's where I get stuck:  I don't exactly understand the concept of eigenspace.  I understand that the wavefunction is generally an eigenfunction and the eignevalue of that eignefunction is the energy from the schrodinger equation.  So I feel I'm missing the link between the wavefunction and eigenspace.  How do the two relate?  What exactly is the meaning of the wavefunction, other than it can be used inside the schrodinger equation?

Some of these basics are holding me up in the class so I'm hoping someone can throw me down the basics in "simple" terms.

Thanks!

Eigenspace is a mathematical concept. It is the space of functions that satisfy an eigenvalue equation: A Psi = a Psi

The wavefunction is a representation of the state of (some) quantum systems.