Adjoint
المؤلف:
Arfken, G
المصدر:
Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, 1985.
الجزء والصفحة:
...
30-5-2018
2247
Adjoint
The word adjoint has a number of related meanings. In linear algebra, it refers to the conjugate transpose and is most commonly denoted 
. The analogous concept applied to an operator instead of a matrix, sometimes also known as the Hermitian conjugate (Griffiths 1987, p. 22), is most commonly denoted using dagger notation 
(Arfken 1985). The adjoint operator is very common in both Sturm-Liouville theory and quantum mechanics. For example, Dirac (1982, p. 26) denotes the adjoint of the bra vector 
as 
, or 
.
Given a second-order ordinary differential equation
 |
(1)
|
with differential operator
 |
(2)
|
where 
and 
, the adjoint operator 
is defined by
Writing the two linearly independent solutions as 
and 
, the adjoint operator can then also be written
In general, given two adjoint operators 
and 
,
 |
(7)
|
which can be generalized to
REFERENCES:
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, 1985.
Dirac, P. A. M. "Conjugate Relations." §8 in Principles of Quantum Mechanics, 4th ed. Oxford, England: Oxford University Press, pp. 26-29, 1982.
Griffiths, D. J. Introduction to Elementary Particles. New York: Wiley, p. 220, 1987.
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