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Q: Relation between angular momentum quantum numbers

We have the angular momentum quantum numbers $(j,l,s)$ representing total angular momentum, orbital angular momentum and spin respectively. I am solving a problem where we try to show that if you have two spin-1 particles then $l+s$ is even. I didn't understand how to relate these numbers toget...

Secret

← 1 message moved from SecretLabs (SE Branch)

Secret

02:43

Infinite time turing machine encoding for fun:

Let blank tape be:

0000000000000000000000000000000000000000000000000...

In shorthand: {}

Any naturals in the brace denote an entry that is 1. Everything else is zero

Succession: {$\forall n, n+1$}

{0}=0

{1}=1

{2}=2

{3}=3

{4}=4

...

{n}=n

Encoding supremum:

Let $a,b,c,..$ be strings for $\alpha_1,\alpha_2,\alpha_3$. Then map all values of a to the odd integers, then map all values of b to every 2nd consecutive unlabelled integer, and so on

Constructing $\omega$

{}

{1}

{1,4}

{1,4,7}

{1,4,7,10}

...

{3n+1} = $\omega$

Constructing $\omega+n$

{3m+n}

Constructing $\omega 2$

{}

user84215

03:44

I am not a crank troll.

Secret

2,5,8,11,14
0th=blank
1st num=1,4,7,10,13,16,19,...
1st slots =1,3,5,7,9,11,13,...
1st encoded = 1,7,13,19,...
2nd slots = 2n entry of complement(1st slot) = 2nd(0,2,3,4,5,6,8,9,10,11,12)
=2,4,6,9,11,...
2nd num = 1st num+1 = 2,5,8,11,14,17,20,...
2nd encoded = common(2nd slots,2nd num) = 2,11,...

3m+1+k=2n+1=>3m+k=2n
k=0: 3m=2n=LCM(2,3)=6. a0=6p+1
k=1: 3m+1=2n=>m odd=>3(2p+1)+2=6p+5

To systemise:

START=blank

Naturals = {n}

omega:

0th=blank

1st num = {0}, 2nd num = {1}, 3rd num = {2},... n+1th num = {n}

1st slot = 2nd(blank) = {1,3,5,7,9,...} = {2m+1}

1st encoded = 1st num(1st slot) = 0->place 1 = {1}

2nd slots = 2nd(blank-1st encoded)=2nd({2,3,4,5,6,....})={2,4,6,8,...}

ERROR

RESTART

START=blank = $\Bbb{N}$

Naturals = {n}

1st slot = 2nd(blank) = {1,3,5,7,9,...} = {2m+1}

1st encoded = 1st slot(1st num) = {2m+1,m=0} = {1}

2nd slot = 2nd (blank - 1st encoded) = 2nd({0,2,3,4,5,6,7,...}) = {2,4,6,8,...} = {2n}

2nd encoded = 2nd slot(2nd num) = {2n,n=1} = {4}

3rd slot = 2nd({0,2,3,5,6,7,...}) = {2,5,7,...}

3rd encoded = {2,5,7,...,n=2} = {7}

nth encoded = {3n+1}

$\omega$ = merge(nth encoded, n in naturals) = {1,4,7,10,13,16,...} = {3n+1}

$\omega + m$ = {3n+m}

1st slot = {2n+1}

1st num = {3n+1}

1st encoded = {2(k-1)+1,3n+1=k} = {2(3n)+1} = {6n+1}

Secret

04:35

2nd slot = 2nd({not 6n+1}) = 2nd({n, n-1 if place = 6k+1}) =2nd (merge ({0},{n+1,n=1-5},{n+2,n=6-13},...) = 2nd({stepfn (n+k,jump = 1st num)} = ?closed form?

Experiment encoding 1:

Naturals = {n}

succession = {n+1}

$\omega$ = {0,n+2}

$\omega + m$ = {m,n+2+m}

$\omega 2$ = {0,1,n+2}

$\omega 2 + m$ = {m,m+1,n+2+m}

$\omega 3$ = {0,n+3}

=FAIL

Naturals = {n}

Succession = {n+1}

$\omega$ = {0,n+2}

$\omega + m$ = {m,n+2+m}

$\omega 2$ = {0,n+3}

$\omega m$ = {0,n+m}

$\omega^2$ = {0,1,n+3}

$\omega^2 m$ = {0,1,n+3+m}

$\omega^2 + m$ = {m,1+m,n+3+m}

FAIL

Naturals = {n}

Succession = {n+1}

$\omega$ = {0,n+2}

$\omega + m $ = {m,n+2+m}

$\omega 2$ = {0,n+3}

$\omega 2 + m$ = {m,n+3+m}

$\omega 3$ = {0,n+4}

$\omega m$ = {0,n+m}

$\omega^2$ = {0,1,n+3}

$\omega^2 + m$ = {m,1+m,n+3+m}

$\omega^2 + \omega$ = {0,1,n+4}

$\omega^2 2$ = {0,2,3,4,n+5}

cannot read...

00000000000000000000000000000000

10000000000000000000000000000000

01000000000000000000000000000000

00100000000000000000000000000000

...

10100000000000000000000000000000

01010000000000000000000000000000

00101000000000000000000000000000

00010100000000000000000000000000

...
01001000000000000000000000000000

01000100000000000000000000000000

01000010000000000000000000000000

01000001000000000000000000000000

...

(space)

01101000000000000000000000000000

01010100000000000000000000000000

01001010000000000000000000000000

01000101000000000000000000000000

...

01110100000000000000000000000000

01011010000000000000000000000000

...

01001101000000000000000000000000

01000110100000000000000000000000

01000011010000000000000000000000

...

01110100000000000000000000000000

01111010000000000000000000000000

01111101000000000000000000000000

01111110100000000000000000000000

...

10100000000000000000000000000000 = $\epsilon_0$

10101000000000000000000000000000

10101010000000000000000000000000

...

nope: 10101000000000000000000000000000 = $\epsilon_0$

10010101000000000000000000000000

10010010101000000000000000000000

10010010010101000000000000000000

...

10001001010100000000000000000000

10001000100101010000000000000000

10001000100010010101000000000000

...

10000100101010000000000000000000 = $\epsilon_0^{\omega}$

...
00001100101010000000000000000000 = $\epsilon_0^{\epsilon_0}$

00011100101010000000000000000000

00111100101010000000000000000000

...

11000100101010000000000000000000 = $\epsilon_1$

11011000100101010000000000000000

11011011000100101010000000000000

...

10000100010010100000000000000000 = $\epsilon_{\omega}$

ERROR: STACK OVERFLOW

Adám

14:48

⎕←{⍺ ⍵}⌺3 3⊢3 4⍴⍳12

AquariusOne

@Adám
┌─────┬────────┐
│1 1  │0 0 0   │
│     │0 1 2   │
│     │0 5 6   │
├─────┼────────┤
│1 0  │0 0 0   │
│     │1 2 3   │
│     │5 6 7   │
├─────┼────────┤
│1 0  │0 0 0   │
│     │2 3 4   │
│     │6 7 8   │
├─────┼────────┤
│1 ¯1 │0 0 0   │
│     │3 4 0   │
│     │7 8 0   │
└─────┴────────┘
┌─────┬────────┐
│0 1  │0 1  2  │
│     │0 5  6  │
│     │0 9 10  │
├─────┼────────┤
│0 0  │1  2  3 │
│     │5  6  7 │
│     │9 10 11 │
├─────┼────────┤
│0 0  │ 2  3  4│
│     │ 6  7  8│
│     │10 11 12│
├─────┼────────┤

Adám

← 2 messages moved from APL

Secret

16:00

Adám

16:33

#TIO alias message #help Dyalog APL Language Elements

AquariusOne

@Adám Added alias for #help

Erik the Outgolfer

#help

AquariusOne

Dyalog APL Language Elements

Erik the Outgolfer

why you didn't ping me :(

#TIO alias message #ref Reference Card

AquariusOne

@EriktheOutgolfer you do not have permission to edit settings for this room!

Erik the Outgolfer

16:35

@Adám please re-post my message above ^^ :)

that is, if you'd like

Adám

#TIO alias message #help %handle% Dyalog APL Language Elements

AquariusOne

@Adám Added alias for #help

Adám

#TIO alias message #ref %handle% Dyalog APL Reference Card

AquariusOne

@Adám Added alias for #ref

Adám

#help

AquariusOne

16:36

@Adám Dyalog APL Language Elements

Adám

#ref

AquariusOne

@Adám Dyalog APL Reference Card

Erik the Outgolfer

#help

AquariusOne

@EriktheOutgolfer Dyalog APL Language Elements

Erik the Outgolfer

#ref

AquariusOne

16:37

@EriktheOutgolfer Dyalog APL Reference Card

Erik the Outgolfer

phew

#TIO alias view

AquariusOne

@EriktheOutgolfer you do not have permission to edit settings for this room!

Adám

17:25

#TIO alias message #docs %handle% Dyalog APL Documentation

AquariusOne

@Adám Added alias for #docs

Uriel

17:43

#docs

AquariusOne

@Uriel Dyalog APL Documentation

Adám

17:55

#TIO alias message #about %handle% You can evaluate an APL expression by typing it into chat prefixed by ⍞←. Use ⎕← instead for boxing display and multi-line results. Do not use markdown. Commands: #lb for language bar, #help for table of language elements, #docs for full documentation, #ref for PDF reference card.

AquariusOne

@Adám Added alias for #about

Adám

#tio alias message #lb %handle%

← +-×÷*⍟⌹○!? |⌈⌊⊥⊤⊣⊢ =≠≤<>≥≡≢ ∨∧⍲⍱ ↑↓⊂⊃⊆⌷⍋⍒ ⍳⍸∊⍷∪∩~ /\⌿⍀ ,⍪⍴⌽⊖⍉ ¨⍨⍣.∘⍤@ ⍞⎕⍠⌸⌺⌶⍎⍕ ⋄⍝→⍵⍺∇& ¯⍬

AquariusOne

@Adám Added alias for #lb

Adám

#about

AquariusOne

@Adám You can evaluate an APL expression by typing it into chat prefixed by ⍞←. Use ⎕← instead for boxing display and multi-line results. Do not use markdown. Commands: #lb for language bar, #help for table of language elements, #docs for full documentation, #ref for PDF reference card.

Adám

17:58

#TIO alias message #about %handle% You can evaluate an APL expression by typing it into chat prefixed by ⍞←. Use ⎕← instead for boxed display and multi-line results. Do not use markdown. Commands: #lb for language bar, #help for table of language elements, #docs for full documentation, #ref for PDF reference card.

AquariusOne

@Adám Added alias for #about

Adám

← 36 messages moved from APL

Adám

20:17

⍞←{⍵⍴⍳}10

AquariusOne

@Adám

Adám

← 2 messages moved from APL

Henry WH Hack v2.1

area51.stackexchange.com/reputation

~~I think I hacked the site.~~ I just was typing in random urls.

It works.

Wait my reps dropped.

OK I don't care but I this seems cool.

2,000 reps was kind of boring anyway.

@kenorb But I clicked recal.

I am more worried about my proposal than my reps now.

I think I know why my reps dropped:

Prepare meta post.

Wait I am confuse.

I went here:

area51.stackexchange.com/reputation

clicked recal and boom!!!

kenorb It's a good thing I did this before you because: you would of lost your reps man I saved you.

I wonder what else I can find.

Ahhh I get it now since some of my post got deleted my reps was suppose to drop so I did it manually.

I am feeling like a mod right now. :)

I am going and take a bath be right back.

OK.

Bye.

I'm back!

Wait: I just lost over 200 reps and I am still calm. @kenorb I am controlling my inner emotions!!! :)

But still I thought only mods can recalc.

kenorb

20:57

Lots of reads, I don't know where to start.

Henry WH Hack v2.1

@kenorb Take it from the top man.

BTW:

18 mins ago, by Henry WH Hack v2.1

Wait: I just lost over 200 reps and I am still calm. @kenorb I am controlling my inner emotions!!! :)

Usually I would of been panicking but I'm not this time.

Henry WH Hack v2.1

21:10

@kenorb Well are you reading?

We have been waiting for the next beta since: Augur.

← 8 messages moved from Paranormal

Diego Henriquez

22:12

What is the real topic ?

Henry WH Hack v2.1

@DiegoHenriquez Of?

Henry WH Hack v2.1

23:21

!!/reload-all

rebooting system..........................................................................‌..............................................................

reloading all modules.........................................................................‌..............................................................

updating brain

completed

@kenorb HELP I LOST 220 REPS!!! WHHHHYYYY???

Somehow I can't panic about it.

I think it's because my brain hasn't come to the point where it notice the lost there for the panic mode is not actives.

in , 19 secs ago, by Henry WH Hack v2.1

I am being more honest by clicking that button you know. ;)

Transcript for