By Emilio d'Emilio, Luigi E. Picasso
This moment version of a very well-received ebook offers greater than 250 nonrelativistic quantum mechanics difficulties of various trouble with the purpose of delivering scholars didactic fabric of confirmed price, permitting them to try their comprehension and mastery of every topic. The assurance is intensely wide, from subject matters on the topic of the drawback of classical physics via achievements in the framework of recent atomic physics to full of life debated, interesting elements in relation to, for instance, the EPR paradox, the Aharonov-Bohm impression, and quantum teleportation. in comparison with the 1st variation, various advancements were made and extra themes of curiosity integrated, particularly targeting trouble-free power scattering. the issues themselves diversity from ordinary and easy ones to people who are advanced yet might be thought of crucial simply because they tackle questions of exceptional value or points more often than not missed in primers. The ebook bargains scholars either a good device for self sustaining studying and a ready-reference consultant they could go back to later of their careers.
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Extra resources for Problems in Quantum Mechanics: with Solutions
Example text
The Sagnac effect was first measured for light in 1925 (Michelson et al. using an interferometer with lx = 613 m and ly = 340 m ) and for neutrons in 1979 (Werner et al. with the above given area). 6 A pointlike light source S is located at a distance D from a screen in which a small circular pin hole of diameter a has been made. The emitted light, whose wavelength is λ, is recorded on a photographic plate parallel to the screen a distance L away from it. S r D L 32 3 Waves and Corpuscles a) Making use of diffraction theory and not paying attention to factors of the order of unity, estimate the dimension of the spot produced on the photographic plate.
B) Calculate the uncertainty Δp in the momentum of the emitted photons and, as a consequence, the uncertainty Δν in their frequency. What is the value of the frequency ν ? The value of Δν calculated above is the natural width of the yellow line of sodium. 2). d) Calculate the energy E and the uncertainty ΔE for the emitted photons; express your results in eV. 1 a) If λ is the wavelength in glass, owing to n = λ0 /λ, one has: 2π 2π 2π(n − 1) d− d= d. 4◦ . b) Let E(x, t) = E0 cos(k x − ω t) be the electric field of the incident wave (the polarization is not relevant).
5 × 104 K . 3 × 10−2 eV . 4 1840 b) From the Bragg relation 2 d sin θ = n λ with n = 1 one obtains: λ ˚. 9 A 2 sin θ c) The number of angles for which there occurs Bragg reflection is the integer part of 2d/λ, namely 2 . 1 × 10−3 K . 8 × 10−6 150 ˚ A. 67 (note that n < 1 ). λi = λf Ef /Ei = 900 d) Note that, contrary to the convention used in optics, here the incidence angle is measured from the reflection plane. So total reflection occurs for angles θ < θr where cos θr = n, namely θ < 48◦ . Equivalently, if p0 is the momentum of the neutron in vacuum and p is the momentum in the medium, taking the y axis normal to the surface and the x axis in the plane containing the incident beam, one has: 2 2 p0y py2 p2 p0x + = x + + V0 .