The wavefunction inside a long barrier (i.e., 0 → ∞) of barrier height V is (psi...
The wavefunction inside a long barrier (i.e., 0 → ∞) of barrier height V is (psi = N e^-kx). A. What is the probability that the particle is inside the barrier? Select from one of the choices below. Please show all work. Thank You!
A) (N^2) / k
B. (N^2 times V) / 2k
C. (N^2) / 2k
D. (N^2 times V) / k
Homework Answers
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The wavefunction inside a long barrier (i.e., 0 → ∞) of barrier
height V is (psi...
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Please thoroughly explain these answers. the correct answers are marked, but i do not understand....
please thoroughly explain these answers. the correct answers are
marked, but i do not understand. also, when is the perturbation
theory preferred over the variation theory and why?
Question A: A particle of mass m in a box of length a has a potential energy inside the box that can be expressed as a linear function of position, i.c, v -kx, where k is a constant. (Assume that the system can be treated using perturbation theory)mo v 1. What would...
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2.5
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mechani mie The potential energy barrier shown below is a simplified model of thec electrons in metals. The metal workfunction (Ew), the minimum energy required to remove an electron from the metal, is given by Ew-,-E where 1s the height of the potential energy barrier and E is the energy of the electrons near the surface of the metal. The potential energy barrier is = 5 eV V(x) V=0 (a) The wavefunction of an electron on the surface (x< 0)...
(III) Quantum Tunneling Consider an electron in 1D in presence of a potential barrier of width L represented by a step function ſo I<0 or 1>L V U. r>0 and 2<L The total wavefunction is subject to the time-independent Schrödinger equation = EV (2) 2m ar2 +V where E is the energy of the quantum particle in question and m is the mass of the quantum particle. A The total wavefunction of a free particle that enters the barrier from...
please thoroughly explain these answers. the correct answers are
marked, but i do not understand. also, when is the perturbation
theory preferred over the variation theory and why?
Question A: A particle of mass m in a box of length a has a potential energy inside the box that can be expressed as a linear function of position, i.c, v -kx, where k is a constant. (Assume that the system can be treated using perturbation theory)mo v 1. What would...
Q4. Consider the 1D infinite square-well potential shown in the figure below. V(x) O0 Position (a) State the time-independent Schrödinger equation within the region 0<x<L for a particle with positive energy E 2 marks] (b) The wavefunction for 0<x< L can be written in the general form y(x) = Asin kx + B cos kx. Show that the normalised wavefunction for the 1D infinite potential well becomes 2sn'n? ?snT/where ( "1,2,3 ! where ( n = 1,2,5, ). [4 marks]...
Consider a particle of mass in a 10 finite potential well of height V. the domain – a < x < a. a) Show that solutions for – a < x < a take the form on (x) = A cos(knx) for odd n, and on (x) = A sin(knx) for even n. . Show a) Match the boundary conditions at x = a to prove that cos(ka) = Bk where k is the wave vector for -a < x...
2.2 Two-level system A particle in the box is described by the following wavefunction 1 1 V(x, t) + V2 V2 = Um(x)e -i(Em/h) In other words, this state is a superposition of two modes: n-th, and m-th. A superposition that involves only two modes (not necessarily particle in the box modes, but any two modes) is called a "two-level system”. A more modern name for such a superposition is a "qubit”. a) Come up with an expression for the...
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2.5
ty which will be discussed in chapter 4 2.3 Consider a particle of mass m subject to a one-dimensional potential V(x) that is given by V = 0, x <0; V = 0, 0<x<a; V = Vo, x> Show that bound (E < Vo) states of this system exist only if k cotka = -K where k2 = 2mE/12 and k' = 2m(Vo - E)/h4. 2.4 Show that if Vo = 974/2ma, only one bound state of the system...
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