2. Determine Va in Figure 2. 2k 6k M 10v - 4k 1000 lx Figure 2
4. (a) A particle in 1D has the wavefunction (x) = Ce-ex?12, where e > 0 and you may assume C > 0. i) Find the normalisation constant C. [4 marks] ii) For small e > 0, show that y is approximately a zero eigenvector of the momentum operator Ộ, i.e., show that lim lôy || = 0. €0+ Hint: for a > 0, recall that Se-ax?dx = Vola and Sox?e-ax?dx = Vra-312 [6 marks] (b) Let Ê be a...
Prove: Let k be a positive integer, and set n :=2k-1(2k – 1). Then (2k+1 – 1)2 = 8n +1 Prove: Let n be a positive integer, and let s and t be integers. Show that Hire (st) = n(s) in (t) mod n.
I. [15 marks] Apply ST/2(0, π/2) and ST/4(0, π/2) to sin x dx, 0 where Sh(a, b) is Simpson's rule applied to the interval [a, b] with hb a. Use s,/2 (0, π/2) and Sn4 (0, π/2) to compute an error estimate for STT/4 (0,7/2). Comment on the quality of the error estimate. I. [15 marks] Apply ST/2(0, π/2) and ST/4(0, π/2) to sin x dx, 0 where Sh(a, b) is Simpson's rule applied to the interval [a, b] with...
V1 Vo1 AD8eS V2 V02 D825 R1-0.5k, R2-2k, R3 0.4k, R4 1k, R5 5k, V1 10v, V2 5v Calculate V01-?, VO2-? and show how to calculate. All voltages is in reference to ground. Assume that both operation amplifier is ideal, and supply voltages is +20v.
B= 0 VCC=10V The emitter current of Q1 is: Rc 315 A) 365 A B) 965 A C) 1.97 mA D) 2 mA OVc=? 10K The collector voltage Vc is: R3 A) -4.8 V B) -0.7 V C) 0.7 V D) 2.9 V w VCC=-100
find laplace transform f(t) = {0, 0 st < 2 t2-1 t2 2 f(t) = {0, 0 st
8. Find the sum of the infinite series: a. 9/2 b.2k/9 C.-2k/9 d. 2/9 e.9k/2
0 loe 10,L 0 10v Ou 301
2. Consider an electron in a 1D potential box (V(x) = 0 for 0<x<L, V(x) = co otherwise) of length L = 1 nm. The electron is described by the wave function, c) = Jasin ( (a) Using the appropriate Hamiltonian derive an expression for the kinetic energy of the electron (5 marks) (b) Calculate the energy (in Joules) of the transition between the ground state and the 1 excited state. [3 marks]