Mathematica Asked by Jacob Hilbert on December 1, 2020
I was trying to implement some tools to do commutators on quantum mechanics, just for fun. Then I noted a peculiarity:
In[1] := TensorExpand[(-ℏ).a]
Out[1] := ℏ (-1).a
Which is not typical of any Symbol
:
In[1] := TensorExpand[(-b).a]
Out[1] := -b.a
I did a little test based on this answer to obtain a fair amount of special symbols:
codes = Table[
ToString[FromCharacterCode[u], InputForm,
CharacterEncoding -> "Symbol"], {u, 0, 65535}];
lnames = Flatten@StringCases[codes, "\[" ~~ __ ~~ "]"];
symbols = Quiet[ToExpression[lnames]] /. {$Failed | Null -> Nothing};
And then which symbols came out of Dot
with TensorExpand
:
In[5] := Cases[Map[TensorExpand[(-#).a] &, symbols], Except[Times[-1, _]]]
Out[5] := {ℏ (-1).a, E (-1).a, (-I).a, (-I).a}
I get that TensorExpand
cannot figure out the dot product with -I
, and that it takes away the E
, as it has certain algebraic properties hard coded into it, but to me it seems weird that despite having different properties:
In[6] := {Head[E], NumericQ[E]}
Out[6] := {Symbol, True}
In[7] := {Head[ℏ], NumericQ[ℏ]}
Out[7] := {Symbol, False}
They are treated as the same by this TensorExpand
thing.
Could you give me an insight on this special behaviour of ℏ
?
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