# Quantum Logic in Algebraic Approach (Fundamental Theories of

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Schrödinger's insight,[ citation needed ] late in 1925, was to express the phase of a plane wave as a complex phase factor using these relations: As the curvature increases, the amplitude of the wave alternates between positive and negative more rapidly, and also shortens the wavelength. For a plane wave in three space dimensions, the wave is represented in a similar way, A(x, t) = A0 sin(k · x − ωt), (5.2) where x is now the position vector and k is the wave vector. If the matter wave to the left of the discontinuity is ψ1 = sin(k1x x+k1y y−ω1 t) and to the right is ψ2 = sin(k2x x + k2y y − ω2 t), then the wavefronts of the waves will match across the discontinuity for all time only if ω1 = ω2 ≡ ω and k1y = k2y ≡ ky.

Pages: 243

Publisher: Springer; 1998 edition (January 31, 1998)

ISBN: 0792349032

Particles and Fields (CRM Series in Mathematical Physics) (Volume 16)

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