Modern Physics For Scientists And Engineers
2nd Edition
ISBN: 9781938787751
Author: Taylor, John R. (john Robert), Zafiratos, Chris D., Dubson, Michael Andrew
Publisher: University Science Books,
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Chapter 7, Problem 7.4P
To determine
String’s transverse velocity.
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Sketch f(y) versus y. Show that y is increasing as a function of t for y < 1 and also for y > 1. The phase line has upward-pointing arrows both below and above y = 1. Thus solutions below the equilibrium solution approach it, and those above it grow farther away. Therefore, ϕ(t) = 1 is semistable.
Legrende polynomials
The amplitude of a stray wave is defined by:
SO) =x
(21+ 1) exp li8,] sen 8, P(cos 8).
INO
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2. Compute Vhat* psi - assume V operator is 1/2w^2x^2
3. Write out Hbar*psi and identify terms so Hber*psi=E*psi is true
4. From cancellation find a
5. insert back a to Schrodinger eq above and find E
Chapter 7 Solutions
Modern Physics For Scientists And Engineers
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- The system has a particle (its mass is m) in the vacuum, no potential energy (V(x) = 0). The Hamiltonian of the system ħ² 8² is given by Ĥ = -2m dx² The initial wave functions at time t = 0 is where a is a real constant. Question #1: Find the time depended wave functions V(x, t) = ? Question #2: Also, for the wave function (x, t) (that has been found above), find the probability current density defined as Note: +∞ 1000 +∞ [too where ã and ß are complex constants; v (z,t = 0) = (=) *exp(- 02²) 1 j = 2 2m 8 (¥* (x)pV(x) + V(x) (pV(x))*) r+∞ 88 da exp(-ã+²) = √ dx dr exp (-ãx² - ikx) = = √= exp(-1/²) dk exp (-²+ ika) = √³ exp(-82²) 4 ax²+bx+c = a (x + = a (x + 2)² + c - 50 2a 4a carrow_forwardWe've looked at the wavefunction for a particle in a box. Soon we will look at other systems with different constraints and types of motion, which have a different wavefunction. For example, a particle rotating on a ring has w(0) = 1 eimo where m= 0, ± 1, + 2,... and ø is the angle of rotation (analagous to x in the particle in a box problems). For -n? d? 21 do2 rotational motion the kinetic energy operator is E, where I is the moment of inertia (analagous to mass). Use the Schrödinger equation to calculate the energy of this particle if V = 0. E= 2m h?m? E= 21 m2 E = 21 h?m² E= 21arrow_forwardLet V = 6+ j8 and I = -(2 + j3). (a) Express V and I in phasor form, and find (b) VI, (c) VI*, (d) V/I, and (e) VV/I.Note: express results of (b) - (e) in both complex numbers (with real and imaginary parts) and phasor forms (with amplitude and phase angle). %3Darrow_forward
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