Understanding the Probability Density Function of a Wave Function

[thinker]

Have known a wave function, how get does distributing density function of the probability?

 

[dextercioby]

You mean,if you have \Psi(\vec{r},t) [/tex],how does one get probablility density...?<br /> Simple:<br /> \mathbb{P}=:|\Psi (\vec{r},t)|^{2}<br /> <br /> Daniel.<br /> <br /> P.S.Or was the question about something else...?<img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f615.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":confused:" title="Confused :confused:" data-smilie="5"data-shortname=":confused:" />

 

[thinker]

thank you, Exactly I want

 

[thinker]

You mean,if you have \Psi(\vec{r},t) [/tex],how does one get probablility density...?<br /> Simple:<br /> \mathbb{P}=:|\Psi (\vec{r},t)|^{2}<br /> <br /> Daniel.<br /> <br /> <br /> P.S.Or was the question about something else...?<img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f615.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":confused:" title="Confused :confused:" data-smilie="5"data-shortname=":confused:" />

<br /> <br /> I want to know the relation between \mathbb{P} and energy.<br /> And formula of underneath in:<br /> &lt;br /&gt; \newcommand{\pd}[2]{\mathbb{P}({#1},{#2})}&lt;br /&gt; \mathbb{I}=\idotsint \frac {\pd {\vec{r}} {t}} {\pd {\vec{r}_m} {t_m}} \cdot (1-ln(\frac {\pd {\vec{r}} {t}} {\pd {\vec{r}_m} {t_m}})) \,D \vec{r} \,dt&lt;br /&gt;<br /> <br /> Among them, \mathbb{P}(\vec{r},t) at \vec{r}= {\vec{r}}_m and t= t_m take the biggest value.<br /> <br /> Is the relation between \mathbb{I} and energy the inverse ratio relation?

 

[dextercioby]

I've never seen your formula...Is it somehow linked to quantum statistics...?In quantum statistics,we don't use Dirac's description of quantum states,but rather von Neumann's...

Please give more details.

Daniel.

 

[thinker]

I've never seen your formula...Is it somehow linked to quantum statistics...?In quantum statistics,we don't use Dirac's description of quantum states,but rather von Neumann's...

Please give more details.

Daniel.

I never heard" the von Neumann".May you tell me information for " the von Neumann"?
It is a quantum statistics.That formula useds for measuring the uncertainty.I doubt it to become the inverse ratio with energy.

 

[thinker]

dextercioby,
You are to did not see which formula, because it is what I create.

 

[dextercioby]

You mean the fluctuation.Fluctuation in what...?That would account for it.What do you mean you created it...?

Did u study QM or SM...?If not,that would explain why u never heard of John von Neumann and why your formula has 99.99% chances of being incorrect.

Daniel.

 

[thinker]

what is QM or SM?
Is John von Neumann who is a mathematician?I don't know this name how to write on my mother tongue.
My formula is correct!

 

[Nylex]

QM = Quantum Mechanics
SM = I'm guessing Statistical Mechanics

 

[thinker]

N_v=\frac {cosv\piJ_v(z)-J_[-v}(z)}{sinv \pi}<br /> Neumann function.<br /> Is he this Neumann?<br /> I am study QM and math and computer

 

[dextercioby]

Nope,that guy is a German.John von Neumann was a Hungary-born American.Mathematician,the one which axiomatized and mathematically founded Quantum Mechanics and Quantum Statistics...

Daniel.

 

[thinker]

You mean the fluctuation.Fluctuation in what...?That would account for it.What do you mean you created it...?

Did u study QM or SM...?If not,that would explain why u never heard of John von Neumann and why your formula has 99.99% chances of being incorrect.

Daniel.

N_v=\frac {cosv{\pi}J_v(z)-J_{-v}(z)} {sinv \pi}
Neumann function.
Is he this Neumann?
I am study QM and MATH and computer.
D \vec{r}=dx\,dy\,dx in my formula.
I think that my formula is right.You can point out it wrong at where?
hehe..It is what I define.

 

[dextercioby]

I've already told you,that is other Neumann.This quy has nothing to do with QM and QSM...

Daniel.

 

[thinker]

I've already told you,that is other Neumann.This quy has nothing to do with QM and QSM...

Daniel.

Perhaps I do not have what you study deep, but I am study QM and MATH and computer.

 

[thinker]

Nope,that guy is a German.John von Neumann was a Hungary-born American.Mathematician,the one which axiomatized and mathematically founded Quantum Mechanics and Quantum Statistics...

Daniel.

I don't knew what you say.I don't read understand.I am sorry.

 

[thinker]

dextercioby,
You did not see understand my formula, these are all not strange.Because you do not understand the information theory.It is the outcome that the information theory combines with the quantum mechanics.

 

[BlackBaron]

Just curiosity thinker, where are you from and what's your mother tongue?

 

[thinker]

Just curiosity thinker, where are you from and what's your mother tongue?

my mother tongue is Chinese.