Bracket VS wavefunction notation in QM

[weirdoguy]

I don't understand it as a whole, because I don't know what you're trying to do. Why are you using bra vector instead of ket?

$<base|[i_1](a_{arguments\ of\ wavefunction})=\delta(v(i_1)-a_{arguments\ of\ wavefunction})$

That is not conventional, or (imo) even correct.

 

[olgerm]

I don't understand it as a whole

i_1'th base vector, that returns value $\delta(v(i_1)-a_{arguments\ of\ wavefunction})$ if its arguments are $a_{arguments\ of\ wavefunction}$.

 

[weirdoguy]

So why are you using bra there? You seems to be hella confused. You should study a few (not one) textbooks first.

 

[vanhees71]

$<base|[i_1](a_{arguments\ of\ wavefunction})=\delta(v(i_1)-a_{arguments\ of\ wavefunction})\\ v(i_1)[i_2]=\sum_{i_3=-\infty}^{\infty}(2^{i_3}*((\lfloor i_1*2^{-2*i_3*A+i_2} \rfloor\mod_2)+\sqrt{-1}*(\lfloor i_1*2^{-2*i_3*A+i_2+1} \rfloor\ mod_2)))$$\delta$ is a function that returns 1 if its argument is 0-vector and 0 otherwise.

$\lfloor \rfloor$ is floor function.

$<base|[i_1]$ is i'th basevector.since $\sigma$ is not 0 only if $v=a_{arguments\ of\ wavefunction}$, value of basefunction is 1 only in case of 1 choice of arguments and otherwise it's value is 0. How every $i_2$'th component of v for $i_1$'th basevectors is calculated is shown in 2. equation.
I tried to write it as easily as I could. I think I used now only conventional symbols.

How can these be "conventional symbols". I've no clue, where one should find them in any textbook or paper. I cannot make any sense of them :-(.

 

[vanhees71]

i_1'th base vector, that returns value $\delta(v(i_1)-a_{arguments\ of\ wavefunction})$ if its arguments are $a_{arguments\ of\ wavefunction}$.

A wave function for a spinless particle, as treated in the QM 1 lecture, in conventional notation is
$$\psi(\vec{x})=\langle \vec{x}|\psi \rangle.$$
Here $|\psi \rangle$ is a Hilbert-space vector (usually normalized to 1, i.e., $\langle \psi|\psi \rangle=1$) and $\langle \vec{x}|$ is the generalized eigen-bra of the position operator. In this sense it's indeed conventional that the bras in the definition of the wave function contains the argument of the wave function.

BTW: From which book/manuscript are you studying? Where did you get your notation, which is far from conventional and for me completely incomprehensible.

 

[olgerm]

Since my intention is to understand bracket notation(and its relation to normal notation), I did not formulate my equations by using bracket notation, but I used normal convetional mathematical notations. I used as simple notation as I could and explained meaning of some symbols.

 

[weirdoguy]

I used as simple notation as I could and explained meaning of some symbols.

And yet it's convoluted and unreadable.

 

[olgerm]

Main point is that for every possible arguments $a_{arguments\ of\ wavefunction}$ there is one basefunction that is 1 with these arguments and 0 with other arguments.

 

[HomogenousCow]

The terminology and notation you're using is not standard, nobody really understands what you're saying. Look at a typical QM or linear algebra textbook and use the notation and terminology that they use in there.

 

[vanhees71]

Since my intention is to understand bracket notation(and its relation to normal notation), I did not formulate my equations by using bracket notation, but I used normal convetional mathematical notations. I used as simple notation as I could and explained meaning of some symbols.

Again to put it very clearly: You don't use anything, I've ever seen in the literature. It's unreadable. I don't even know, what you want to write!

You can write QT completely without bras and kets. E.g., Weinberg doesn't use the bra-ket notation at all. However his books are highly readable (and among the best newer textbooks I'm aware of).

 

[olgerm]

Which symbols you do not undersatand? I did not invent any original notation, but used mathematical normal notation. I really do not know how to express these relations using more ordinary notation.
If you really do not understand - can you describe me a example of basevectors. by writing
$\vec{e_{base}} [i ] = ...$, where ## \vec{e_{base}} ##, is i'th basevector. Maybe I could reformulate my equations to be similar to yours.

 

[weirdoguy]

can you describe me a example of basevectors

Base vectors of which space?

 

[olgerm]

Base vectors of which space?

The ones that can be used here

We have some basis set of functions $\phi_n$ and the components of $\psi$ are the terms $c_n$ in the sum:
$$\psi = \sum_{n}c_{n}\phi_{n}$$