PHY2D_Quiz7

# PHY2D_Quiz7 - in front of the wave function) and energies...

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QUIZ 7 PHYSICS 2D SPRING QUARTER 2009 Professor S.K.Sinha Formulas and constants Mass of electron m e = 9.1. 10 -31 kg Charge on electron = 1.6.10 -19 C Planck’s Constant h= 6.626. 10 -34 J.s =4.136. 10 -15 eV.s h = h / 2 ! = 1.055.10 " 34 J . s = 6.582.10 " 16 eV . s 1 eV =1.6. 10 -19 J Coulomb’s constant k = 1/ (4 !" 0 ) = 8.99.10 9 N . m 2 / kg 2 Velocity of light c = 3.10 8 m/s Energy of photon E = hf For photon λ f = c Compton formula λ′ - λ = (h/m e c)(1 – cos ϕ ) Bragg’s Law n λ =2 d sin θ (n=1,2,……) Bohr’s quantization for Angular momentum mvr = n h Bohr radius a 0 =0.529. 10 -10 m 1 Rydberg (Energy required to ionize hydrogen atom) =13.6 eV Rydberg Constant R = 1.097. 10 7 m -1 Force due to Electric field : F = q E Force due to Magnetic Field: F = q vxB Momentum operator p = ! i h " " x Stationary Schrodinger Equation ! h 2 2 m d 2 " dx 2 + U ( x ) = E 1. Consider a particle of mass m moving in a one-dimensional box with infinitely high potential walls at x= - L/2 and x = L/2. (a) Write down the wave functions (including the normalization constant

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Unformatted text preview: in front of the wave function) and energies for the states n=1 and n=2. (b) write down the values of x at which the probability of finding the particle is greatest for each of these 2 states. (c) Use these wave functions to calculate the average values of p, &amp;lt;p&amp;gt; and of p 2 , &amp;lt; p 2 &amp;gt; for each of these states. and hence p which is [&amp;lt; p 2 &amp;gt; -&amp;lt;p&amp;gt; 2 ] 1/2 for each of these states, where p is the momentum of the particle. (15 pts) 2. Show that the function ! ( x ) = C xe &amp;quot; # x 2 is a solution of the stationary Schrodinger Equation for a potential function of the form U ( x ) = 1 2 m 2 x 2 where m is the particle mass and is a constant, provided has a particular value and find the value of and the energy of this state. Note: This not the ground state wave function! (10 pts) SHOW ALL DETAILS OF YOUR DERIVATIONS!...
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## This note was uploaded on 12/07/2009 for the course PHYS phys 2d taught by Professor Hirsch during the Spring '08 term at UCSD.

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PHY2D_Quiz7 - in front of the wave function) and energies...

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