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Mathematics for Quantum Physics
lectures
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bb32fdb0
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bb32fdb0
authored
2 years ago
by
Maciej Topyla
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Update src/6_eigenvectors_QM.md
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@@ -67,7 +67,11 @@ the rules of matrix multiplication:
This relations follows from the eigenvalue equation in terms of components
$$
\s
um_{j=1}^n A_{ij} v_j =
\l
ambda v_i
\,
,
\q
uad
\t
o
\q
uad
\s
um_{j=1}^n A_{ij} v_j -
\s
um_{j=1}^n
\l
ambda
\d
elta_{ij} v_j =0
\,
,
\q
uad
\t
o
\q
uad
\s
um_{j=1}^n
\l
eft( A_{ij} -
\l
ambda
\d
elta_{ij}
\r
ight) v_j =0
\,
.
\b
egin{array}{r}
\s
um_{j=1}^n A_{ij} v_j =
\l
ambda v_i
\,
,
\\
\t
o
\q
uad
\s
um_{j=1}^n A_{ij} v_j -
\s
um_{j=1}^n
\l
ambda
\d
elta_{ij} v_j =0
\,
,
\\
\t
o
\q
uad
\s
um_{j=1}^n
\l
eft( A_{ij} -
\l
ambda
\d
elta_{ij}
\r
ight) v_j =0
\,
.
\e
nd{array}
$$
Therefore the eigenvalue condition can be written as a set of coupled linear equations
$$
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