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--- documentation:language_reference:functions:ytokmatrix [2018/09/25 13:42]
Simon Heinze created
+++ documentation:language_reference:functions:ytokmatrix [2018/09/25 16:28] (current)
Simon Heinze Filled with content
@@ Line 2: / Line 2: @@
 ###
-alligned paragraph text
+YtoKMatrix($orb$) takes the angular momentum $l$ or the name of a non-relativistic atomic orbital and returns the corresponding matrix to rotate from a basis of spherical harmonics to cubic harmonics. It is also possible to give a list of $l$ numbers or orbital names, in which case the output is a block diagonal matrix with the rotation matrices as entries.
 ###
 ===== Input =====
-  * bla : Integer
+  * $orb$ : An integer number, or a list of integer numbers, or a string that can be interpreted as a non-relativistic atomic orbital, or a list or strings.
-  * bla2 : Real
+  * Options:
+     * "addSpin" : bool determining if spin-space is considered in the matrix (resulting in matrices double in size). (Default true)
 ===== Output =====
-  * bla : real
+  * $R$ : Rotation Matrix from a basis of spherical to cubic harmonics.
 ===== Example =====
-###
-description text
-###
 ==== Input ====
 <code Quanty Example.Quanty>
--- some example code
+print("")
+print("YtoKMatrix(0)")
+print(YtoKMatrix(0))
+print("")
+print("YtoKMatrix(\"s\", {{\"addSpin\",false}})")
+print(YtoKMatrix("s", {{"addSpin",false}}))
+print("")
+print("YtoKMatrix(1)")
+print(YtoKMatrix(1))
+print("")
+print("YtoKMatrix(\"p\")")
+print(YtoKMatrix("p"))
+print("")
+print("YtoKMatrix(2)")
+print(YtoKMatrix(2))
+print("")
+print("YtoKMatrix(\"d\")")
+print(YtoKMatrix("d"))
+print("")
+print("YtoKMatrix({0,1,2}, {{\"addSpin\",false}})")
+print(YtoKMatrix({0,1,2}, {{"addSpin",false}}))
+print("")
+print("YtoKMatrix({\"s\",\"p\",\"d\"}, {{\"addSpin\",false}})")
+print(YtoKMatrix({"s","p","d"}, {{"addSpin",false}}))
+print("\n\n")
+print("A more realistic example")
+Orbitals = {"1s","2s","2p"}
+Indices, NF = CreateAtomicIndicesDict(Orbitals)
+--Some Operator definition on spherical harmonics
+op = NewOperator("U", NF, Indices["2p_Up"], Indices["2p_Dn"],{0,1})
+print("Operator on a basis of spherical harmonics")
+print(op)
+opK = Rotate(op, YtoKMatrix(Orbitals))
+print("Operator on a basis of cubic harmonics")
+print(opK)
 </code>
 ==== Result ====
 <file Quanty_Output>
-text produced as output
+YtoKMatrix(0)
+{ { 1 , 0 } ,
+  { 0 , 1 } }
+YtoKMatrix("s", {{"addSpin",false}})
+{ { 1 } }
+YtoKMatrix(1)
+{ { 0.70710678118655 , 0 , 0 , 0 , -0.70710678118655 , 0 } ,
+  { 0 , 0.70710678118655 , 0 , 0 , 0 , -0.70710678118655 } ,
+  { (0 + 0.70710678118655 I) , 0 , 0 , 0 , (0 + 0.70710678118655 I) , 0 } ,
+  { 0 , (0 + 0.70710678118655 I) , 0 , 0 , 0 , (0 + 0.70710678118655 I) } ,
+  { 0 , 0 , 1 , 0 , 0 , 0 } ,
+  { 0 , 0 , 0 , 1 , 0 , 0 } }
+YtoKMatrix("p")
+{ { 0.70710678118655 , 0 , 0 , 0 , -0.70710678118655 , 0 } ,
+  { 0 , 0.70710678118655 , 0 , 0 , 0 , -0.70710678118655 } ,
+  { (0 + 0.70710678118655 I) , 0 , 0 , 0 , (0 + 0.70710678118655 I) , 0 } ,
+  { 0 , (0 + 0.70710678118655 I) , 0 , 0 , 0 , (0 + 0.70710678118655 I) } ,
+  { 0 , 0 , 1 , 0 , 0 , 0 } ,
+  { 0 , 0 , 0 , 1 , 0 , 0 } }
+YtoKMatrix(2)
+{ { 0.70710678118655 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.70710678118655 , 0 } ,
+  { 0 , 0.70710678118655 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.70710678118655 } ,
+  { 0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 } ,
+  { 0 , 0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 } ,
+  { 0 , 0 , (0 + 0.70710678118655 I) , 0 , 0 , 0 , (0 + 0.70710678118655 I) , 0 , 0 , 0 } ,
+  { 0 , 0 , 0 , (0 + 0.70710678118655 I) , 0 , 0 , 0 , (0 + 0.70710678118655 I) , 0 , 0 } ,
+  { 0 , 0 , 0.70710678118655 , 0 , 0 , 0 , -0.70710678118655 , 0 , 0 , 0 } ,
+  { 0 , 0 , 0 , 0.70710678118655 , 0 , 0 , 0 , -0.70710678118655 , 0 , 0 } ,
+  { (0 + 0.70710678118655 I) , 0 , 0 , 0 , 0 , 0 , 0 , 0 , (0 - 0.70710678118655 I) , 0 } ,
+  { 0 , (0 + 0.70710678118655 I) , 0 , 0 , 0 , 0 , 0 , 0 , 0 , (0 - 0.70710678118655 I) } }
+YtoKMatrix("d")
+{ { 0.70710678118655 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.70710678118655 , 0 } ,
+  { 0 , 0.70710678118655 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0.70710678118655 } ,
+  { 0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 } ,
+  { 0 , 0 , 0 , 0 , 0 , 1 , 0 , 0 , 0 , 0 } ,
+  { 0 , 0 , (0 + 0.70710678118655 I) , 0 , 0 , 0 , (0 + 0.70710678118655 I) , 0 , 0 , 0 } ,
+  { 0 , 0 , 0 , (0 + 0.70710678118655 I) , 0 , 0 , 0 , (0 + 0.70710678118655 I) , 0 , 0 } ,
+  { 0 , 0 , 0.70710678118655 , 0 , 0 , 0 , -0.70710678118655 , 0 , 0 , 0 } ,
+  { 0 , 0 , 0 , 0.70710678118655 , 0 , 0 , 0 , -0.70710678118655 , 0 , 0 } ,
+  { (0 + 0.70710678118655 I) , 0 , 0 , 0 , 0 , 0 , 0 , 0 , (0 - 0.70710678118655 I) , 0 } ,
+  { 0 , (0 + 0.70710678118655 I) , 0 , 0 , 0 , 0 , 0 , 0 , 0 , (0 - 0.70710678118655 I) } }
+YtoKMatrix({0,1,2}, {{"addSpin",false}})
+{ { 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 } ,
+  { 0 , 0.70710678118655 , 0 , -0.70710678118655 , 0 , 0 , 0 , 0 , 0 } ,
+  { 0 , (0 + 0.70710678118655 I) , 0 , (0 + 0.70710678118655 I) , 0 , 0 , 0 , 0 , 0 } ,
+  { 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 , 0 } ,
+  { 0 , 0 , 0 , 0 , 0.70710678118655 , 0 , 0 , 0 , 0.70710678118655 } ,
+  { 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 , 0 } ,
+  { 0 , 0 , 0 , 0 , 0 , (0 + 0.70710678118655 I) , 0 , (0 + 0.70710678118655 I) , 0 } ,
+  { 0 , 0 , 0 , 0 , 0 , 0.70710678118655 , 0 , -0.70710678118655 , 0 } ,
+  { 0 , 0 , 0 , 0 , (0 + 0.70710678118655 I) , 0 , 0 , 0 , (0 - 0.70710678118655 I) } }
+YtoKMatrix({"s","p","d"}, {{"addSpin",false}})
+{ { 1 , 0 , 0 , 0 , 0 , 0 , 0 , 0 , 0 } ,
+  { 0 , 0.70710678118655 , 0 , -0.70710678118655 , 0 , 0 , 0 , 0 , 0 } ,
+  { 0 , (0 + 0.70710678118655 I) , 0 , (0 + 0.70710678118655 I) , 0 , 0 , 0 , 0 , 0 } ,
+  { 0 , 0 , 1 , 0 , 0 , 0 , 0 , 0 , 0 } ,
+  { 0 , 0 , 0 , 0 , 0.70710678118655 , 0 , 0 , 0 , 0.70710678118655 } ,
+  { 0 , 0 , 0 , 0 , 0 , 0 , 1 , 0 , 0 } ,
+  { 0 , 0 , 0 , 0 , 0 , (0 + 0.70710678118655 I) , 0 , (0 + 0.70710678118655 I) , 0 } ,
+  { 0 , 0 , 0 , 0 , 0 , 0.70710678118655 , 0 , -0.70710678118655 , 0 } ,
+  { 0 , 0 , 0 , 0 , (0 + 0.70710678118655 I) , 0 , 0 , 0 , (0 - 0.70710678118655 I) } }
+A more realistic example
+Operator on a basis of spherical harmonics
+Operator: Coulomb Operator
+QComplex         =          0 (Real==0 or Complex==1 or Mixed==2)
+MaxLength        =          4 (largest number of product of lader operators)
+NFermionic modes =         10 (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis)
+NBosonic modes   =          0 (Number of bosonic modes (phonon modes, ...) in the one particle basis)
+Operator of Length   4
+QComplex      =          0 (Real==0 or Complex==1)
+N             =         25 (number of operators of length   4)
+C  5 C  4 A  5 A  4 | -3.999999999999999E-02
+C  7 C  5 A  7 A  5 |  2.000000000000000E-01
+C  6 C  5 A  6 A  5 |  7.999999999999999E-02
+C  7 C  4 A  7 A  4 |  7.999999999999999E-02
+C  6 C  4 A  6 A  4 |  2.000000000000000E-01
+C  9 C  5 A  9 A  5 |  2.000000000000000E-01
+C  8 C  5 A  8 A  5 | -3.999999999999999E-02
+C  9 C  4 A  9 A  4 | -3.999999999999999E-02
+C  8 C  4 A  8 A  4 |  2.000000000000000E-01
+C  7 C  6 A  7 A  6 | -1.600000000000000E-01
+C  9 C  7 A  9 A  7 |  2.000000000000000E-01
+C  8 C  7 A  8 A  7 |  7.999999999999999E-02
+C  9 C  6 A  9 A  6 |  7.999999999999999E-02
+C  8 C  6 A  8 A  6 |  2.000000000000000E-01
+C  9 C  8 A  9 A  8 | -3.999999999999999E-02
+C  6 C  5 A  7 A  4 |  1.200000000000000E-01
+C  7 C  4 A  6 A  5 |  1.200000000000000E-01
+C  8 C  5 A  7 A  6 | -1.200000000000000E-01
+C  9 C  4 A  7 A  6 |  1.200000000000000E-01
+C  8 C  5 A  9 A  4 |  2.400000000000000E-01
+C  9 C  4 A  8 A  5 |  2.400000000000000E-01
+C  7 C  6 A  8 A  5 | -1.200000000000000E-01
+C  7 C  6 A  9 A  4 |  1.200000000000000E-01
+C  8 C  7 A  9 A  6 |  1.200000000000000E-01
+C  9 C  6 A  8 A  7 |  1.200000000000000E-01
+Operator on a basis of cubic harmonics
+Operator: Coulomb Operator
+QComplex         =          0 (Real==0 or Complex==1 or Mixed==2)
+MaxLength        =          4 (largest number of product of lader operators)
+NFermionic modes =         10 (Number of fermionic modes (site, spin, orbital, ...) in the one particle basis)
+NBosonic modes   =          0 (Number of bosonic modes (phonon modes, ...) in the one particle basis)
+Operator of Length   4
+QComplex      =          0 (Real==0 or Complex==1)
+N             =         27 (number of operators of length   4)
+C  5 C  4 A  5 A  4 | -1.599999999999999E-01
+C  7 C  6 A  5 A  4 | -1.200000000000000E-01
+C  7 C  4 A  7 A  4 |  7.999999999999997E-02
+C  6 C  5 A  7 A  4 |  1.200000000000000E-01
+C  7 C  4 A  6 A  5 |  1.200000000000000E-01
+C  6 C  5 A  6 A  5 |  7.999999999999997E-02
+C  5 C  4 A  7 A  6 | -1.200000000000000E-01
+C  7 C  6 A  7 A  6 | -1.599999999999999E-01
+C  9 C  5 A  9 A  5 |  1.999999999999999E-01
+C  9 C  7 A  9 A  7 |  1.999999999999999E-01
+C  8 C  5 A  8 A  5 |  7.999999999999997E-02
+C  8 C  7 A  8 A  7 |  7.999999999999997E-02
+C  9 C  4 A  9 A  4 |  7.999999999999997E-02
+C  9 C  6 A  9 A  6 |  7.999999999999997E-02
+C  8 C  4 A  8 A  4 |  1.999999999999999E-01
+C  8 C  6 A  8 A  6 |  1.999999999999999E-01
+C  7 C  5 A  7 A  5 |  1.999999999999999E-01
+C  6 C  4 A  6 A  4 |  1.999999999999999E-01
+C  9 C  8 A  9 A  8 | -1.600000000000000E-01
+C  8 C  5 A  9 A  4 |  1.200000000000000E-01
+C  8 C  7 A  9 A  6 |  1.200000000000000E-01
+C  9 C  4 A  8 A  5 |  1.200000000000000E-01
+C  9 C  6 A  8 A  7 |  1.200000000000000E-01
+C  5 C  4 A  9 A  8 | -1.200000000000000E-01
+C  7 C  6 A  9 A  8 | -1.200000000000000E-01
+C  9 C  8 A  5 A  4 | -1.200000000000000E-01
+C  9 C  8 A  7 A  6 | -1.200000000000000E-01
 </file>

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