By Speakman J
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Sample text
The function u(t, z) = Be−[(z−st)/ z] is a wave pulse propagating through the medium with the velocity s. By using the Fourier transform of u, present this wave field as a sum of plane waves. 10. Consider visible (yellow) light with the wavelength λ = 600 nm (600 × 10−9 m). Assume a light wave propagating in free space with the intensity density I = 1 mW cm−2 (10−3 J s−1 cm−2 ). Calculate the electric field amplitude F0 (in units of V cm−1 ). Find the wavevector, photon momentum, and energy. Estimate the density of quanta Nq,b .
One of the important properties of solutions to Eq. 6) where δi j = 1, 0, if i = j, if i = j. The major task of quantum mechanics is to solve the Schr¨odinger wave equation, Eq. 1). As we have mentioned already, the wavefunction of a particle in free space (V (r) = 0) has a plane-wave form (r, t) = Aei(kr− t) (Eq. 43)). 1 Three types of solutions of the Schr¨odinger equation for a one-dimensional well of arbitrary form. 7) E = -h = 2m 2m which coincides with the classical relationship between the particle’s momentum, p, and its energy, E.
To estimate the particle wavelength and to understand the consequences of the uncertainty principle, let us assume that a free electron moves with a velocity of about 107 cm s−1 . 2 × 10−7 cm = 72 A. 2 × 10−6 cm = 720 A. greater than the wavelength of the electron! According to our estimates, we see that electron wavelengths have very small values. For a material particle with a larger mass, the wavelength is even smaller. That is why in most cases of ordinary life we do not observe wave-like behavior of particles.