Suppose a particle with a definite energy is going in empty space from a location r_1 to a location r_2. In other words, it is a free particle with no forces on it. Except for a numerical factor in front, the amplitude to go from r_1 to r_2

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2022-08-20

Suppose a particle with a definite energy is going in empty space from a location r 1 to a location r 2 . In other words, it is a free particle with no forces on it. Except for a numerical factor in front, the amplitude to go from r 1 to r 2 is
(3.7) r 2 | r 1 = e i p r 12 r 12 .

Answer & Explanation

Rachael Trevino

Rachael Trevino

Beginner2022-08-21Added 9 answers

Feynman's expression
(3.7) G ( r )   =   r 2 | r 1   =   exp ( i k r ) r
is the propagator/Greens function
( 2 + k 2 ) G ( r )   =   4 π δ 3 ( r )
for the 3D Helmholtz equation/the free TISE.

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