- The award of the 1964 Nobel Prize in physics to C. - The temperature of the sun is about T ¼ 5800K 20(300K). - The electric field should vanish at both ends of the cavity. - for the z component of the wave vector. - In the most favorable situation the lower level (level 1) of the laser transition is empty. - These factors are reflected in the size of the ampli- fication or gain coefficient a. - (1.5.1) nor (1.5.2) can be solved independently of the other. - However, several consequences of the quantum theory are essential. - In the Coulomb field of the. - In the Bohr model a state of the electron is characterized by the quantum number n.. - there are n possible values of the orbital angular momentum quantum number. - The origin of the binding. - In terms of the reduced mass. - The ground level of the oscillator corresponds to n ¼ 0. - in (2.3.11), that is, by the shape of the potential function V(x). - The vibrational spectra of the two isotopic molecules for the same electronic transition E e ! E e 0. - This was before the quantum mechanical derivation by Heisenberg (1925) of the formula (2.3.8) for the energy. - It is found that the rotational energy (2.4.2) of the molecule has the allowed values. - This is a general feature of the quantum theory of angular momentum. - Figure 2.10 The first few vibrational energy levels of the CO 2 molecule.. - E g , where hn is the frequency of the radiation). - Specifically, an electron to the right of the hole indicated in Fig. - 2.16) as the current of the electrons in the conduction band. - In particular, the energy of the lowest energy state should be. - According to these relations, the product N n N p is the same for the two sides of the junction.. - c (x) ¼ u(x)e ikx , (2:A:5a) with k a real number and u(x) now not a constant, but a function with the periodicity of the potential:. - This is the limit of the potential of Fig. - Figure 2.33 Plot of the left side of Eq. - this is implicit in the assumption of the periodicity of the potential. - The rate of change of the electron energy as a result of this force is. - Now the force equals the rate of change of the momentum p ¼ h k:. - The acceleration of the electron is therefore. - Thus, m arises from the proportionality of the electron acceleration to the external force. - gives the Balmer series of the hydrogen spectrum. - In what region of the spectrum are these wavelengths?. - p , where n is the refractive index of the LED, and estimate this factor for GaAs. - The binding energy of the ion H 2 þ. - (a) What is the contribution to the energy from the Coulomb repulsion of the nuclei?. - (b) What is the contribution to the energy from the Coulomb attraction of the electron to the nuclei?. - Figure 3.1 Absorption lines of the sun’s atmosphere. - F ¼ e(E þ v B where e and v are the charge and velocity, respectively, of the particle.. - Figure 3.3 The position vectors r e and r n of the electron and nucleus, measured from some origin O.. - is the reduced mass of the electron – nucleus system.. - The vector analog of the Taylor series is. - is the electric dipole moment of the electron – nucleus pair. - In the Appendix we show that the electron oscillator model can be regarded as a good approximation to the quantum theory of the interaction of an atom with light.. - dt ¼ 0, i.e., the total number of atoms N 1 þ N 2 in the upper and lower states of the transition stays the same.. - The peak value of the absorption rate is. - Far out in the wings of the Lorentzian, where jn n 0 j d n 0 , there is very little absorption. - (3.4.35) for absorption in terms of the spontaneous emission rate A 21 for the E 2 ! E 1 transition. - The narrower the width of S(n), the easier it is to satisfy (3.5.4). - The historical significance of the Planck spectrum in the development of quantum. - “classical limit” of the Planck spectrum.. - 3.13, how- ever, only a small part of the radiation from the heated filament lies in the visible.. - (3.7.5) are the foundation for a considerable part of the theory of lasers.. - 3pe 0 h c 3 jx m 1 m 2 j where x m 1 m 2 is the matrix element between states m 1 and m 2 of the electron coordinate x. - (For a multielectron atom, x is the sum of the position vectors of all the electrons.) In the case of g 2. - and will examine the solution of the S equation, d. - under the following interpretation of the effect of collisions.. - (3.8.4) for the collisionless displacement, except for the appearance of the new g c term. - The linewidth of the collision-broadened lineshape is [Eq. - Collisions completely interrupt the phase of the oscillation. - It is convenient to express this in terms of the atomic (or molecular) weights M X and M Y. - e 4(nn 0 ) 2 ln 2=dn 2 D , (3:9:9) and we recognize that d n D is the width (FWHM) of the Doppler absorption curve, since (Fig. - (3:9:12) for the ratio of the Doppler width to the resonance frequency is also useful.. - Each peak falls in the remote wing of the other function (see Fig. - will result in a (homogeneous) linewidth of the form (3.11.2). - populations are independent of the field intensity. - Figure 3.20 Absorption cross section of the sodium D 2 line [Eq. - (3.13.9)] for different values of the temperature T. - (3.14.6) in which the field frequency v is very large compared to any of the transition frequencies v j. - where 1 b ¼ n 2 b e 0 is the dielectric permittivity of the background. - and introducing the oscillator strength f of the resonant transition, we have. - while the expectation value of the electron coordinate is. - h z 2 12 E, (3 : A : 22) where k z l ¼ k x l ^ z is the component of k x l along the direction of the electric field. - Does your estimate indicate that molecular vibrations lie in the infrared region of the spectrum?. - (1.5.2)? What is the physical meaning of the differences in the form of these two equations?. - where I n (0) is the spectral brightness of the radiation input to the cell.. - [Note that the spectrum of the emitted radiation is identical to the absorption lineshape S(n. - I n (L) 2hn 3 =c 2 e hn=k B T 1 , where T is the temperature of the medium.. - In Chapter 1 the growth rate of the number of laser photons in the cavity was described by an amplification coefficient a. - Each of the mirrors of Fig. - number of atoms in level 2 is n 2 ¼ N 2 V g , where V g is the volume of the gain medium.. - Likewise the total number of atoms in the lower level of the laser transition is n 1 ¼ N 1 V g . - ¼ PN as a result of the pumping process. - 2 hn 31 N T G which, because of the approximation DN t N T , is the same as (4.7.15). - We further assume that the intensity I n of the field is constant in time. - where we have used A s 2 1 for the spontaneous emission rate of the sodium D 2 line (Section 3.13). - The FWHM radiative linewidth of the sodium D 2 line is [Eq. - The electromagnetic energy density u is proportional to the square of the electric field: 3. - sin 2 kz or, in terms of the intensity I n . - interference of the two traveling-wave fields. - Thus, g(n) varies with z on the scale of the laser wavelength.. - Saturation of the absorption or gain coefficient is more complicated in the case of inhomogeneous broadening. - Consider the saturation of the gain coefficient when there is Doppler broadening. - (b) Determine the steady-state values of the three level populations.. - Usually, only one of the mirrors is transmitting (Fig. - This ratio is called the quantum efficiency of the three-level laser. - Similarly n 0 / n 30 is the quantum efficiency of the ideal four-level laser. - (t þ s)I (þ) ¼ 1 2 (t þ s)I ¼ g t lI: (5:4:5) Note that the one-way intensity I n (þ) ¼ I = 2 in the direction of the output mirror is inde- pendent of z