On wave matrices, and some properties of the wave equation
1936 ◽
Vol 157
(890)
◽
pp. 1-27
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Keyword(s):
1—Wave matrices became important in wave theory as the result of the use of them made by Dirac to express the operator of the second order wave equation as the square of a linear one, and hence obtain a first order equation. Thus, p 2 representing the second order operator, the equation p 2 Ψ = 0, may be factorized, and written (∑ E α p α ) (∑ E α p α ) Ψ = 0, (α = 1, 2, . . . , n ), giving the first order equation ∑ E α p α Ψ = 0, (1) if the p α commute with themselves and with the E α , and if the E α are matrix roots of +1 or of —1, which satisfy E α E β = — E β E a (β ≠ α). (2)
2018 ◽
1934 ◽
Vol 145
(855)
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pp. 645-656
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2014 ◽
Vol 56
(5)
◽
pp. 1218-1228
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Keyword(s):
A stochastic collocation method for the second order wave equation with a discontinuous random speed
2012 ◽
Vol 123
(3)
◽
pp. 493-536
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2015 ◽
Vol 2015
◽
pp. 1-11
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Keyword(s):
1954 ◽
Vol 222
(1148)
◽
pp. 93-108
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Keyword(s):