a) Determine the quantum mechanical operators for th following: Lx=yPz - ZPy That is, find Îx = ŷpz - 2py where x = x Ly = zpx - xPz Ly = 2px - xpz ŷ = y 2= z Lz = xpy - ypx L = xpy - YPx
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- What type of quantum mechanical problems can be solved using the time-independent Schrödinger equation (TISE)? h^2 dw(x) dx2 + U (x) y (x) = Eµ (x) 2m Any problem where the potential U(x) has no time dependence. O Any quantum mechanical problem can be solved Only problems that have a constant potential U (x) = Uo Any problem where the energy values E are positive O Any problem where the energy values E are negativeAngular Momentum Quantum TheoryAn electron in a one-dimensional infinite potential well of length L has ground-state energy E1.The length is changed to L' so that the new ground-state energy is E'1 = 0.500E1 .What is the ratio L'/L?
- *24 Figure 39-30 shows a two-dimen- sional, infinite-potential well lying in an xy plane that contains an electron. We probe for the electron along a line that bisects L, and find three points at which the detection probability is maximum. Figure 39-30 Problem 24. Those points are separated by 2.00 nm. Then we probe along a line that bisects L, and find five points at which the detection probability is maximum. Those points are sep- arated by 3.00 nm. What is the energy of the electron?For full credit, show the starting equation in symbols. If it makes sense, solve in symbols before plugging in numerical values. Remember, physical quantities with units have to have the units written down. Unless otherwise stated, keep enough sig-figs to produce a final answer accurate to three sig-figs 1. X-rays with a wavelength of 4 =8.55 pm are used in a Compton scattering experiment (i.e. the photons are scattered by essentially free electrons). a. What is the energy, E, , of the incident photons in eV? b. When the Compton scattered X-ray scatters to an angle (measured from the direction of the incident X-ray) of 0 = 115.0°, what is the wavelength of the Compton scattered X-ray? c. When the Compton scattered X-ray scatters to an angle (measured from the direction of the incident X-ray) of 0 =115.0°, what is the change in energy for the X-ray photon in eV? d. When the Compton scattered X-ray scatters to an angle (measured from the direction of the incident X-ray) of 0 =115.0°,…a) [2018] State Kirchhoff’s two Laws, and give the fundamental physical principles which each law expresses. b) De Broglie explained the Bohr model of the hydrogen atom by attributing a wavelength λ toa particle, with the value of λ coming from the momentum p = mv as λ = h/p.i) Calculate the de Broglie wavelength of a bird (a racing pigeon) that weighs 0.350 kgand flies at 100 km per hour.ii) Equating the centripetal force on an electron orbiting around a proton with the Coulomb force gives the expression v2 = e2/(4πε0mer). Calculate the speed of an electron or- biting at the Bohr radius, rB = 0.053 nm.iii) Calculate the momentum and the de Broglie wavelength of an electron moving at the speed you obtain in (ii).iv) Compare the wavelength you obtain in (iii) with the circumference of the orbit. Com- ment on this comparison. Explain briefly what it implies about the possible orbits of the Bohr model and how the higher orbits might be predicted. c) Thorium-234 is…
- A LiBr molecule oscillates with a frequency of 1.7×1013 Hz. (a) What is the difference in energy in eV between allowed oscillator states? (b) What is the approximate value of n for a state having an energy of 1.0eV?Can you help solve this questionA quantum simple harmonic oscillator consists of an electron bound by a restoring force proportional to its position relative to a certain equilibrium point. The proportionality constant is 8.11 N/m. What is the longest wavelength of light that can excite the oscillator? ps:- answer is not 443.68
- [QUANTUM PHYSICS]A quantum system is described by a wave function (r) being a superposition of two states with different energies E1 and E2: (x) = c191(r)e iEit/h+ c292(x)e¯iE2t/h. where ci = 2icz and the real functions p1(x) and p2(r) have the following properties: vile)dz = ile)dz = 1, "0 = rp(x)T#(x)l& p1(x)92(x)dx% D0. Calculate: 1. Probabilities of measurement of energies E1 and E2 2. Expectation valuc of cnergy (E)Suppose that you have a 2D quantum system where X and Px are the x- component position and momentum operators and Y and Py are the y- component position and momentum operators. Which of the following commutators is not equal to 0? [Py,Y] O IX,Y] O [Px,Px] O [PxY]