Consider the wavefunction for a particle in a one-dimensional box when the level is n = 6. Calculate the total probability of finding the particle between x = 0 and x = L/12? Provide your answer to three significant figures.

Consider the wavefunction for a particle in a one-dimensional box when the level is n = 6. Calculate the total probability of finding the particle between x = 0 and x = L/12? Provide your answer to three significant figures.

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter40: Quantum Mechanics

Section: Chapter Questions

Problem 18P

See similar textbooks

Related questions

Q: Consider an electron of energy 1 eV that encounters a potential barrier of width 0.1nm and energy…

Q: ) Simple quantum systems: potential barrier Consider a uniform potential barrier of height vp = 6 eV…

A: (1) for alpha particleEquation for transmission probability;…

Q: A one-dimensional infinite well of length 200 pm contains an electron in its third excited state.We…

A: a) The wave function of an electron in an infinite one-dimensional potential well of length L along…

Q: A particle is confined to the one-dimensional infinite potential well of If the particle is in its…

Q: A particle is in the ground state of a box of length L (i.e. an infinite potential well). Suddenly…

A: Solution:As given that A particle is in the ground state of a box of length L (i.e. an infinite…

Q: A potential barrier of height V extends from x = 0 to positive x. Inside this barrier the normalized…

A: (a) Probability of finding the particle inside the barrier

Q: A particle moving in one dimension has the wave function Y(x, t) = Aeli(ax-bt)] %3D where a and b…

Q: Show that the wavelength predicted for a particle in a one-dimensional box of length L from the de…

A: For a box of length L and V=0 in this length, we can write Schrodinger equation -h2mdψ2dx2=Eψ…

Q: The wavefunction of an electron is given by 1≤x≤ 16 y(x) = c = 0 x 16 where c is a positive real…

A: Probability of given wave function

Q: An electron is trapped in a finite potential well that is deep enough to allow the electron to exist…

Q: equation for the particle in a one-dimensional box, the quantization of energy levels results when…

A: Schrodinger wave equation for the particle in a one dimensional box is : δ2ψδx+8π2mh2E-vψ=0

Q: Find the probability of the state |0) and |1) |) = (1 – 2i) |0) + 3i |1 .

A: Let us first normalize the given wave function. Let |ψ> denote the normalized wave function of…

Q: An electron is trapped in a one-dimensional infinite potential well that is 170 pm wide; the…

Q: the wave function everywhere.

Q: Which of the following changes would increase the probability of transmission of a particle through…

Q: Consider the wave function phi(x) = A sin(kx) where k = 2pi/lambda and A is a real constant. (a)…

Q: Consider a particle in a box with edges at x = ±a . Estimate its ground state energy using…

A: We have a trial wave function, ψ=|x|λ-aλ. The energy is given by,<E>=<ψ|H|ψ><ψ|ψ>…

Q: Find the expectation value of kinetic energy E for the = 2 sin(zr) vavefunction (r)

A: Given:- The normalized wavefunction ψ(x) = 2sinπx Find:- The expectation value of kinetic energy…

Q: J. particle in an infinite potential well ait to Ax Given the wwave fonction of a L Ala-x) a/2 E x…

Q: Consider a particle with the following wave-function: ,xL and L and A are constants. (a) What is the…

Q: A wave function of a particle with mass m is given by, Acosa ≤ ≤+ otherwise b(z) = {1 Find the…

A: See step 2 .

Q: Use the Schrödinger equation to calculate the energy of a 1-dimensional particle-in-a-box system in…

A: Problem 1 Wavefunction of particle in a box is given by, ψx=2LsinnπxL

Q: If the absolute value of the wave function of a proton is 2 times as large at location A than at…

Q: As an analogy to wave packets, consider an “automobile packet” that occurs near the scene of an…

A: The automobile packet that occurs near the scene of an accident on a freeway.

Q: a) Find the normalization constant A in terms of the constants a and b. b) Sketch ψ(x, 0) as a…

A: c) From the above graph we can see that the wave function is highest at x=a. That means the…

Q: Q. Aparticle is moving in one-dimension that characterized by the state Iw) with wave function y-Ae…

A: Given:- A particle is moving in one -dimension that is characterized by the state ψ with the wave…

Q: The normalized solution to the Schrodinger equation for a particular potential is ψ = 0 for x =0.…

Q: An electron having total energy E = 4.50 eV approaches a rectangular energy barrier with U = 5.00 eV…

A: (a) To determine the transmission coefficient, first, it needs to determine the constant α by the…

Q: An electron is trapped in a one-dimensional infinite potential well that is 470 pm wide; the…

Q: An electron is trapped in a one-dimensional infinite potential well that is 100 pm wide, the…

A: Given : potential well, L = 100 × 10-12 m ∆x = 5.0 × 10-12 m

Q: Suppose a particle of mass m is moving in a one-dimensional potential of a kind -20<x<2a- = (x)A-…

A: The Energy eigenvalue of a particle inside a potential well of side 'a' is given by: En =n2π2ħ22ma2…

Q: For a "particle in a box" of length, L, draw the first three wave functions and write down the…

A: Given: Length of the box is L. To show: λn = 2 L / n

Q: The expectation value is the strict average of the possible values.

A: The above statement is true

Q: What is the probability of finding a particle in the last 10% of a one-dimensional box for n = 1…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Consider an electron in a 2D harmonic trap with force constants kxx = 232 N/m and kyy = 517 N/m.…

Q: The number of methods for arranging two semi-classical systems on a power slice of 4 states is: O 4…

Q: An electron is trapped in a one-dimensional infinite potential well that is 100 pm wide; the…

Q: The normalization condition for a wavefunction Ψ(x, t) is given by � ∞ −∞ Ψ∗(x, t)Ψ(x, t)dx = 1.…

A: We have a wave function ψ(x,t) which satisfies the Schrodinger wave function given by H^ψ=Eψ where H…

Q: For a particle in a 1-dimensional infinitely deep box of length L, the normalized wave function or…

A: We have to find the probability of finding the particle.

Q: Suppose that in a certain system a particle free to move along one dimension (with 0 ≤ x ≤ ∞) is…

Q: A particle moving in one dimension has the wave function 4(x,t) = Ael(ax-bt)] where a and b are…

Q: Find the lowest energy of an electron confined to move in a three dimensional potential box of…

Q: An Infinite Square Well of width L that is centred around x = 0 is shown in the figure. At t = 0, a…

Q: The wavefunction for the particle in a one-dimensional infinite potential well is given by n²n?h? ()…

Q: Find the excitation energy from the ground level to the third excited level for an electron confined…

Question

100%

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A 12.0-eV electron encounters a barrier of height 15.0 eV. If the probability of the electron tunneling through the barrier is 2.5 %, find its width.
A particle of mass m confined to a box of width L is in its first excited state 2(x). (a) Find its average position (which is the expectation value of the position). (b) Where is the particle most likely to found?
When an electron and a proton of the same kinetic energy encounter a barrier of the same height and width, which one of them will tunnel through the barrier more easily? Why?
A simple model of a radioactive nuclear decay assumes that a-particles are trapped inside a well of nuclear potential that walls are the barriers of a finite width 2.0 fm and height 30.0 MeV. Find the tunneling probability across the potential barrier of the wall for a-particles having kinetic energy (a) 29.0 MeV and (b) 20.0 MeV. The mass of the a -particle is m=6.641027kg.
Suppose that in a certain system a particle free to move along one dimension (with 0 ≤ x ≤ ∞) is described by the unnormalized wavefunction Ψ(x)=e-ax with a = 2 m−1. What is the probability of finding the particle at a distance x ≥ 1 m?
Consider a particle of mass m, located in a potential energy well.one-dimensional (box) with infinite height walls. The wave function that describes this system is:Ψn(x) = K sin (nπx /L), for 0 ≤ x ≤ LΨn(x) = 0 for any other value.K is a constant and n = 1,2,3,... Determine K*K = │K│2
The wavefunction for a quantum particle tunnelling through a potential barrier of thickness L has the form ψ(x) = Ae−Cx in the classically forbidden region where A is a constant and C is given by C^2 = 2m(U − E) /h_bar^2 . (a) Show that this wavefunction is a solution to Schrodinger’s Equation. (b) Why is the probability of tunneling through the barrier proportional to e ^−2CL?
Normalize the wave function ψ= A sin (nπ/a x) by finding the value of the constant A when the particle is restricted to move in a dimensional box of width ‘a’.
At time t = 0 the wave function for a particle in a box is given by the function in the provided image, where ψ1(x) and ψ1(x) are the ground-state and first-excited-state wave functions with corresponding energies E1 and E2, respectively. What is ψ(x, t)? What is the probability that a measurement of the energy yields the value E1? What is <E>?
Consider the wave function for the free particle, as shown. At what value of x is the particle most likely to be found at a given time? (a) at x = 0 (b) at small nonzero values of x (c) at large values of x (d) anywhere along the x axis
A potential barrier of height V extends from x = 0 to positive x. Inside this barrier the normalized wavefunction is ψ = Ne−κx. Calculate (a) the probability that the particle is inside the barrier and (b) the average penetration depth of the particle into the barrier.
Calculate the expectation value of x2 in the state described by ψ = e -bx, where b is a ħ constant. In this system x ranges from 0 to ∞.