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## Main Question or Discussion Point

Okay, so here's my knowledge of quantum mechanics: *crickets chirping in the background*. Here's my mathematical knowledge: basic integral calculus, some multivariable calculus, decent amount of linear algebra (knowledge of subspaces, projections, eigenvalues of matrices, eigenvectors, etc.), a decent amount of diff. eqs (not PDEs, though), all of high school math (extremely well... I was like 3 points of the usamo this year).

So anyways, I started learning quantum mechanics like a week ago, and pretty much have learned:

the construction of the Schrodinger equation (time dependant and independant)

the overall concept of a Hermitian operator

the infinite well situation

and that's about it.

I have been running into the words: eigenvalues, eigenfunctions, and eigenstates many times. I am pretty sure I understand what an eigenvalue and eigenfunction is, but I'm a bit shaky on what an eigenstate is. Just to clarify, in the equation

[tex]

\hat{A}\psi = a \psi

[/tex]

for some [tex]a[/tex], we have that [tex]\psi[/tex] is an eigenfunction (which could be vector-valued?) of [tex]\hat{A}[/tex] and [tex]a[/tex] is an eigenvalue of [tex]\hat{A}[/tex]. Is this correct?

If relevant or helpful at all, I am currently a senior in high school who is going to enter college as a freshman this coming fall.

So anyways, I started learning quantum mechanics like a week ago, and pretty much have learned:

the construction of the Schrodinger equation (time dependant and independant)

the overall concept of a Hermitian operator

the infinite well situation

and that's about it.

I have been running into the words: eigenvalues, eigenfunctions, and eigenstates many times. I am pretty sure I understand what an eigenvalue and eigenfunction is, but I'm a bit shaky on what an eigenstate is. Just to clarify, in the equation

[tex]

\hat{A}\psi = a \psi

[/tex]

for some [tex]a[/tex], we have that [tex]\psi[/tex] is an eigenfunction (which could be vector-valued?) of [tex]\hat{A}[/tex] and [tex]a[/tex] is an eigenvalue of [tex]\hat{A}[/tex]. Is this correct?

If relevant or helpful at all, I am currently a senior in high school who is going to enter college as a freshman this coming fall.