Why explain with both vectors and functions

[mraptor]

Why when explaining/introducing QM things get explained with the <bra|ket> complex vectors... then somewhere in between they start using functions (psi)..
It gets confusing when epxlanation start switching between them back and forth...

My understanding is they are the same thing...
Is there some purpose of this exercise...
Similar thing with the Operators... when the explanation goes around the the braket vectors.. they use matrices... then the moment find operators to be differential operators we switch to functions.

I understand it is logical to do this, but why we don't they stick with one of the mathematical abstraction and go with it the whole time..

sorry if it is a stupid question.. I'm neither mathematician nor physicist.
May be that is why they are confusing to me ;)

 

[strangerep]

I'm neither mathematician nor physicist.

Perhaps you should say what level of maths you do understand, else it's hard to know at what level to pitch an answer. I could say that functions in a Hilbert space are vectors in that space, but I suspect this wouldn't be very enlightening...

 

[maverick_starstrider]

Why when explaining/introducing QM things get explained with the <bra|ket> complex vectors... then somewhere in between they start using functions (psi)..
It gets confusing when epxlanation start switching between them back and forth...

My understanding is they are the same thing...
Is there some purpose of this exercise...
Similar thing with the Operators... when the explanation goes around the the braket vectors.. they use matrices... then the moment find operators to be differential operators we switch to functions.

I understand it is logical to do this, but why we don't they stick with one of the mathematical abstraction and go with it the whole time..

sorry if it is a stupid question.. I'm neither mathematician nor physicist.
May be that is why they are confusing to me ;)

Because a first introduction to quantum mechanics has been somewhat formalized as the introduction to a few specific systems: The particle in the box, the harmonic potential and propagation through a potential barrier (followed by the hydrogen atom in a later course). These are sort of three examples that are considered the "take-away" from a first course in QM. That puts teaching in a place where they want to introduce the more robust and generalized bra-ket notation which you'll need for continued learning in quantum and the fact that these problems specifically are best worked out with integrals and calculus. They want to show you a few classic pictures to give you a sense of the key features of quantum while prepping you for later generalizations.

 

[mraptor]

I see, thank you