The following is an acceptable wavefunctions for a particle in a 2D rectangular box with infinite...
Which of the following are acceptable wavefunctions for a particle in a one-dimensional box? Check all that apply. ψ(x) = C(1 - sin(nπx/a)) ψ(x) = Acos(nπx/a) + Bsin(nπx/a) ψ(x) = E/cos(nπx/a)ψ(x) = D(a - x)xψ(x) = Cx3(x-a)
Which of the following are acceptable wavefunctions for a particle in a one-dimensional box? Check all that apply. ψ(x) = C(1 - sin(nπx/a)) ψ(x) = Acos(nπx/a) + Bsin(nπx/a) ψ(x) = E/cos(nπx/a)ψ(x) = D(a - x)xψ(x) = Cx3(x-a)
3. A particle is in a 1D box (infinite potential well) of dimension, a, situated symmetrically about the origin of the x-axis. A measurement of energy is made and the particle is found to have the ground state energy: 2ma The walls of the box are expanded instantaneously, doubling the well width symmetrically about the origin, leaving the particle in the same state. a) Sketch the initial potential well making it symmetric about x - 0 (note this is different...
Questions 1 - 5 deal with a particle in a one-dimensional infinite square well of width a where 0, 0 SX Sa V(x) = 100, Otherwise. The stationary states are Pn(x) = sin(**) with energies En = "forn = 1,2,3.. Question 1 (14 pts) Which of the following is correct? A. The Hilbert space for this system is one dimensional. B. The energy eigenstates of the system form a ID Hilbert space. C. Both A and B are correct. D....
6. The Particle in a Box problem refers to a potential energy function called the infinite square well, aka the box: ; x < 0 (Region I) V(x) = 0 : 0 L (Region II) x x >L (Region III) Let's investigate a quantum particle with mass m and energy E in this potential well of length L We were unable to transcribe this image6d (continued) write down an equation relating ψ, (x = 0) to ψ"(x I and II....
In solving the particle in a one dimensional infinite depth box problem (0k x < a) we started with the function following is a true statement? (a) The value of k is found by requiring that the solution be normalized. (b) The function wx) is not an eigenfunciton of the operator d2/dx2 (c) It is necessary that this function equals a when x=0 (ie, Ψ(0) = a). (d) The boundary condition at x = 0 is used to show that...
(15) 4. The state of the particle-in-a box located between 0<x<a is described by the following normalized wavefunction at t=0: Y(x,t=0) =(1/2) A Sin (fx/a)-(1/12) A Sin(3 rex/a) + (1/2) A Sin(5tx/a) (10) a) If the energy of the system is measured at t=0, what energies will be observed What is the probability (in percent) of observing an energy E> 9h-/8ma?? on
1 Particle in a Box with a Bump (based on B&J 4.11) Consider a particle of mass m in a 1-D double well with potential given by Vo, 05\x\<b V(x) = { 0, b<\x<c 100, [x]>c . We will study the lowest energy states, for which 0 <E<V, corresponding to tunnelling between the two wells. (a) Write down the time-independent Schödinger equation in the three regions -c<x<-b, –b< <b, and b< I< c. Write down the most general wavefunction solution...
please explain all, thanks! 4. (60 pts) A particle in an infinite square well of width L has an initial wave function (x,t = 0) = Ax(L - x)2, OSX SL a) Find y(x, t) fort > 0. You first have to normalize the wave function. Hint: this is best expressed an infinite series: show that the wave function coefficients are on = * 31% (12 – n?)(1-(-1)") → (n = 87315 (12 - nºre?); n odd. b) Which energy...
8.4 The Two-Dimensional Central-Force Problem The 2D harmonic oscillator is a 2D central force problem (as discussed in TZD Many physical systems involve a particle that moves under the influence of a central force; that is, a force that always points exactly toward, or away from, a force center O. In classical mechanics a famous example of a central force is the force of the sun on a planet. In atomic physics the most obvious example is the hydrogen atom,...