
    \h{                         S SK JrJrJrJr  S SKJr  S SKJr  S SK	J
r
  S SKJr  S SKJrJr  S SKJr  S SKJr  S S	KJrJrJrJr  S S
KJr  \" S5      u  rrrSS jrS rS r S r!S r"S r#g)    )IRationaloopi)S)symbols)exp)sqrt)cossin)	integrate)simplify)R_nlE_nl
E_nl_diracPsi_nlm)raiseszn r Zc                     [        U 5      n [        U5      n[        X-
  5      U:  a  g[        U5      [        U 5      :  a  [        X-
  U-  5      nXB:*  $ [        X-
  U -  5      nXB:*  $ )NT)floatabs)abmax_relative_errormax_absolute_errorrelative_errors        Y/var/www/auris/envauris/lib/python3.13/site-packages/sympy/physics/tests/test_hydrogen.pyfeqr      si    aAaA
15z&&
1vAaeQY // aeQY//    c                     S[         -  n S[        SU S-  -  5      -  [        [        * U -  5      -  [        SSU S-  -  -  5      [        [        * SU -  -  5      -  S[        SU -  -  -
  -  [        R
                  [        SSU S-  -  -  5      -  [        [        * SU -  -  5      -  [        -  U -  [        SS5      [        SSU S-  -  -  5      -  [        [        * SU -  -  5      -  SS[        -  SU -  -  -
  [        SS5      [        U -  S-  -  -   -  [        SS5      [        SSU S-  -  -  5      -  [        [        * SU -  -  5      -  S[        SU -  -  -
  -  [        -  U -  [        SS5      [        SSU S-  -  -  5      -  [        [        * SU -  -  5      -  [        U -  S-  -  [        SS5      [        SU S-  -  5      -  [        [        * SU -  -  5      -  SS[        -  SU -  -  -
  [        SS	5      [        U -  S-  -  -   [        SS
5      [        U -  S-  -  -
  -  [        SS5      [        SSU S-  -  -  5      -  [        [        * SU -  -  5      -  S[        SU -  -  -
  [        SS5      [        U -  S-  -  -   -  [        U -  -  [        SS5      [        SSU S-  -  -  5      -  [        [        * SU -  -  5      -  S[        SU -  -  -
  -  [        U -  S-  -  [        SS5      [        SSU S-  -  -  5      -  [        [        * SU -  -  5      -  [        U -  S-  -  S.
nU H0  u  p#[        [        X#[        [         5      XU4   -
  5      S:X  a  M0   e   g )N                  Q                  P   @      i   #   )
)r    r   )r!   r   )r!   r    )r"   r   )r"   r    )r"   r!   )r%   r   )r%   r    )r%   r!   )r%   r"   r   )	Zr
   r	   rr   Halfr   r   r   )r   Rnls       r   test_wavefunctionr6      sI   	!A$qAv,aRT*Q!Q$Z 3r1Q3x=0A1Q3K@a1a4j))CAaCM9A=a?Aa1a4j!11CAaCMA	
QqS!A#Y!RAaC!83	35B$q!AqD&z"22S!QqS]B	
Q!WB$q"QT'{"33c1"ac(mCqsQhNAa1f-QB!H=	
QqS!A#Y!Q1Q3(2	2Xa5E1q5P	PRB$q!AqD&z"22S!QqS]B	
Q!Wx2!A#1	1367c;B$q!AqD&z"22S!QqS]B	
Q1XA#"C 42ad7#44sA2qs8}D!axO	A" Q1a(1V945::: r   c            	          Sn [        U S-   5       HM  n[        U5       H;  n[        [        X[        5      S-  [        S-  -  [        S[        45      S:X  a  M;   e   MO     g )Nr!   r    r   )ranger   r   r1   r   )n_maxr4   r5   s      r   	test_normr:   4   sW    E519qAT!]A-14q!RjAQFFF  r   c            	         [        S5      n [        S5      n[        S5      n[        SSSXU5      [        U * 5      [        [        5      -  :X  d   e[        SSSXU5      [         R
                  [        U * S-  5      -  U -  [        U5      [        [        * U-  5      -  S[        [        5      -  -  -  :X  d   e[        S	SSXUS5      [        S5      * [        U5      -  [        [        U-  5      -  [        U5      -  S[        [        5      -  -  [        S5      -  S
-  [        S5      -  [        SU -  S	-  5      -  U S-  S-  -  :X  d   eg )Nr1   phithetar    r   r!   r%   r"   r&   r*   )	r   r   r	   r
   r   r2   r   r   r   )r1   r<   r=   s      r   test_psi_nlmr@   ;   sM   fA	%C
G*EAq!QU+sA2wb/AABAAq"ae,#qbAh-1G!1Ku:QBH%T"X628 8 8 8Aq!QUA.47(SZ2Gq3w<3e*3%()DH3689!3=?A3B
z
3 a1.3/23a%A3> > ? >r   c                     [        [        [        5      [        S-  * S[        S-  -  -  :X  d   e[        [        5      SS[        S-  -  -  :X  d   e[        SS5      [        S5      S-  * S-  :X  d   e[        SS5      [        S5      S-  * S-  :X  d   e[        S5      [        R                  * S-  :X  d   e[        S5      [        R                  * S-  :X  d   e[        S5      [        R                  * S-  :X  d   e[        S5      [        R                  * S	-  :X  d   e[        S
5      [        R                  * S-  :X  d   e[        [        S 5        g )Nr!   r>   r    /   r(   r"      r%       d   i N  c                      [        S5      $ Nr   )r    r   r   <lambda>(test_hydrogen_energies.<locals>.<lambda>S   s    tAwr   )r   r4   r0   r   Oner   
ValueErrorrH   r   r   test_hydrogen_energiesrM   F   s#   1:!Q$!Q$'''7b!AqD&k!!!2;1R5!8)V,,,,2;1R5!8)V,,,,7quuffo%%%7quuffo%%%7quuffo%%%7quuffo%%%9))))
:'r   c                     [        SSSSS9S[        S5      -  S-
  :X  d   e[        [        SSSSS9S[        S5      -  S-   [        S[        S5      -  S-   5      -  S	-
  -
  5      S:X  d   e[        [        SSSSS9S
[        S5      -  S-   [        S[        S5      -  S-   5      -  S-
  -
  5      S:X  d   e[        [        SSSSS9SS[        S5      -  -   [        SS[        S5      -  -   5      -  S-
  -
  5      S:X  d   e[        [        SSSSS9SS[        S5      -  -   [        SS[        S5      -  -   5      -  S-
  -
  5      S:X  d   e[        SS5       Hl  n [        U 5       HZ  n[	        [        X5      [        U 5      SS5      (       d   eUS:  d  M2  [	        [        XS5      [        U 5      SS5      (       a  MZ   e   Mn     Sn[        SS5       Hl  n [        U 5       HZ  n[	        [        XUS9[        X5      SS5      (       d   eUS:  d  M1  [	        [        XSU5      [        X5      SS5      (       a  MZ   e   Mn     Sn[        SS5       Hl  n [        U 5       HZ  n[	        [        XUS9[        X5      SS5      (       d   eUS:  d  M1  [	        [        XSU5      [        X5      SS5      (       a  MZ   e   Mn     [        [        S  5        [        [        S! 5        [        [        S" 5        g )#Nr!   r   r    )r0   cr(   r"   r*   rD   r%   6   r&   l      	      iKid i  iB)i9iQI  R   iY<' i/  ixN r+   gh㈵>F)r0   g-C6?gMbP?c                      [        SS5      $ rG   r   rH   r   r   rI   .test_hydrogen_energies_relat.<locals>.<lambda>|   s    z!Q/r   c                      [        SS5      $ )Nr    r>   rW   rH   r   r   rI   rX   }   s    z!R0r   c                      [        SSS5      $ )Nr    r   FrW   rH   r   r   rI   rX   ~   s    z!Q6r   )r   r
   r   r8   r   r   r   rL   )r4   r5   r0   s      r   test_hydrogen_energies_relatr[   V   s&   aa1%47Q666Jq!qA.Ad1gINr$q'zB'4(*+4, - .123 3 3Jq!qA.BtAwJOs47{S()4*,-4. / 0345 5 5
 Jq!qC0i(T
C 79x$t*'<<=6>@E6F G HKLM M MJq!rS1y7UD 8IU(;;<7=?D7E F GJKL L L
 1a[qAz!'a$====1u:aE2DGT4HHHH   	
A1a[qAz!!,d1j$EEEE1u:aE15tAz4NNNN   	
A1a[qAz!!,d1j$EEEE1u:aE15tAz4NNNN   :/0
:01
:67r   N)-q=r\   )$sympy.core.numbersr   r   r   r   sympy.core.singletonr   sympy.core.symbolr   &sympy.functions.elementary.exponentialr	   (sympy.functions.elementary.miscellaneousr
   (sympy.functions.elementary.trigonometricr   r   sympy.integrals.integralsr   sympy.simplify.simplifyr   sympy.physics.hydrogenr   r   r   r   sympy.testing.pytestr   r4   r1   r0   r   r6   r:   r@   rM   r[   rH   r   r   <module>rg      sX    4 4 " % 6 9 ? / , B B '
'
1a0;.G	?( (8r   