De Broglie s equation

C De Broglie s equation that led to thinking of electrons as both particles and waves... 

This equation, called de Broglie s equation, allows us to calculate the wavelength for a particle, as shown in Example 12.2. 

Notice from Example 12.2 that the wavelength associated with the ball is incredibly short. On the other hand, the wavelength of the electron, although quite small, happens to be of the same order as the spacing between the atoms in a typical crystal. This is important because, as we will see presently, it provides a means for testing de Broglie s equation. 

On solving this equation we obtain, instead of de Broglie s equation for free electrons, the equation... 

These equations, in conjunction with de Broglie s equation, enable us to calculate the refractive index /x from the experimental... 

Comparison of de Broglie s equation (see Eq. 4.20) with Bohr s equation (see Eq. 4.22) shows that the wavelength of the standing wave is related to the linear momentum, f, of the electron by the following simple formula ... 

Example 7.5 shows that although de Broglie s equation can be applied to diverse systems, the wave properties become observable only for submicroscopic objects. This distinction is due to the smallness of Planck s constant, h, which appears in the numerator in Equation (7.7). 

Example 7.5 shows that although de Broglie s equation can be applied to diverse systems, the wave properties become observable only for submicroscopic objects. 

This equation applies to all particles from electrons to golf balls. De Broglie s equation was useful in explaining why the energies of electrons in atoms are quantized. 

A = /jc/ photon> h has the form of de Broglie s equation AdB =h/p but is written for radiation instead of matter. We ve used de Broglie s equation to devise a correspondence principle to tell us when we need to use quantum mechanics to describe a system. Does this form of Planck s law suggest a version of the correspondence principle appropriate for radiation ... 

This equation states that the wavelength of a particle is inversely proportional to its momentum, mv, and the proportionality constant is h, Planck s constant. That is, de Broglie s equation implies that a particle of mass m acts as a wave. Only a wave, remember, can have a wavelength. 

X rays. This result verified de Broglie s relationship, at least for electrons. Larger chunks of matter, such as balls, have such small wavelengths (see Sample Exercise 7.3) that they are impossible to verify experimentally. However, we believe that all matter obeys de Broglie s equation. 

Most practicing physicists have learned what little they know of the history of this period by reading textbooks written after the quantum revolution. Often texts and teaehers treat the Planck radiation law, the Einstein photoelectric equatiorr, the Bohr atom and the Compton effect in one sequence assuming that this provides an adequate background for understanding E = hv and p = hv/c [de Broglie s equation]. This can leave a student with less than total respect for the physicists who took so long to see the obvious necessity for this form of quantization (p. 95). 

Before you can appreciate Schrbdinger s solution, there is another point to be emphasized. .. Schrodinger combined de Broglie s equation with classical equations for wave motion. .. The concept of quantization enters Schrodinger s theory naturally with the basic assumption of an electron matter wave. This is in contrast with Bohr s theory, where quantization is imposed as a postulate at the start (Kotz and Purcell 1991, pp. 296-298). 

---