And as Guest has pointed out you have once again included a suspiciously spurious comment in your 'demonstration of understanding' which is both at odds with what it refers to and is completely out of place in the post as a whole. Can you tell us what he's referring to?
Really? Go on, I'll give you another chance....Hows it out of place? How is it spurious, explain how it's spurious? I know what is meant by it, so..?
Here you confused states and operators. You also fail to understand what properties trivially follow from a Hilbert space. Nowhere have I seen you show a working understanding of what a Hilbert space is, so the evidence is you consistently have shown you don't. Its not my fault you can't back up your claims. I keep giving you the opportunity, like giving you a chance to alter what Guest has quoted you saying, but you never step up.before I was accused for lying by yourself and guest, I have shown consistently to know what a frikken Hilbert Space is. It's not my fault you cannot back up your claims.
On the contrary. You've demonstrated that you lack even the understanding needed to paraphrase meaningfully! But please, continue to prove my point...I have shown consistently to know what a frikken Hilbert Space is. It's not my fault you cannot back up your claims.
What does this mean?The finite norm is defined as:
$$<\psi|\psi>= \sum^{\infty}_{n=1} |C_n|^2= ||\psi||^2$$
on the $$\ell$$ finite dimensional space.
You really don't. Not more than a week or two ago, you didn't even know set builder notation, nor how to delimit simple intervals on the real line. I cannot even remember when I was taught the latter, but I believe the former was taught in maths class as the very first thing in my first year in high school (gymnasium). 3 years before I went to university. Where Hilbert spaces was 2nd year material.Don't patronize me, I am quite aware of what a Hilbert Space is.
No, it doesn't.I did put up: You said I lied about knowing what a Hilbert Space was, but my post above contradicts that statement.
Look again:Hows it out of place? How is it spurious, explain how it's spurious? I know what is meant by it, so..?
There's something in this sentence that's very strange if one is familiar with the notation and nomenclature. What is it?The finite norm is defined as:
$$<\psi|\psi>= \sum^{\infty}_{n=1} |C_n|^2= ||\psi||^2$$
on the $$\ell$$ finite dimensional space.
Pot. Kettle. Black.Secondly, this is not what this thread is about; before I was accused for lying by yourself and guest, I have shown consistently to know what a frikken Hilbert Space is. It's not my fault you cannot back up your claims.
It was on my request - I want you to answer my question.
I'm afraid that doesn't make any sense. Care to try again?
Perhaps you could explain what $$\langle \psi | \psi \rangle$$ actually is?
I wonder what I was talking about.
I was speaking about the norm of a vector wasn't I? By memory I can say that you define the definate norm as $$||\psi||=^{def} <\psi|\psi>^{\frac{1}{2}}$$ Which is the positive square root of the positive $$||\psi||$$ side. I'm not aware of what is wrong with this?
For example, knowing such relationships to the probability amplitudes, you can state that $$|\psi>=a-ib$$ and $$<\psi|=a+ib$$ where $$<\psi|\psi>=a^2+b^2$$ making a real positive number.
Ok, that's a good effort. Some slight misunderstandings though; $$| \psi \rangle$$ and $$\langle \psi |$$ are, as you imply, vectors (or to be sightly more pedantic since they abstract as opposed to "real" vectors like force - they are elements of a vector space) and you seems to have equated them to the complex numbers $$a \pm i b$$. Can you please explain what you mean?
Maybe it would be enlightening if you wrote down $$\langle \psi | \psi \rangle$$ in the language of wave mechanics. That way it's pretty clear what you are physically talking about.
GD has read the definition of $$\langle \psi | = (|\psi\rangle)^{\dag}$$, ie the "Take its conjugate" definition, and in an attempt to look like he knows what he's doing he's go to the only bit of complex analysis he knows and done the $$zz* = |z|^{2}$$ formula, probably motivated by the mention of amplitude in the explanation of wave function norms. Hence why he seems to be mixing things up, equating a complex amplitude with a state.Can you please explain what you mean?
What an odd thing to say, since if you'd read books or lecture notes on this stuff you'd have been people do things differently.That was just an example, I never thought about expressing it any other way.