Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Question
Chapter 7.1, Problem 7.1P
(a)
To determine
The first order correction for energy and the reason for the absence of energy for the even value of n.
(b)
To determine
The first three terms in the expansion for the equation 7.13.
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Chapter 7 Solutions
Introduction To Quantum Mechanics
Ch. 7.1 - Prob. 7.1PCh. 7.1 - Prob. 7.2PCh. 7.1 - Prob. 7.3PCh. 7.1 - Prob. 7.4PCh. 7.1 - Prob. 7.5PCh. 7.1 - Prob. 7.6PCh. 7.2 - Prob. 7.8PCh. 7.2 - Prob. 7.9PCh. 7.2 - Prob. 7.10PCh. 7.2 - Prob. 7.11P
Ch. 7.2 - Prob. 7.12PCh. 7.2 - Prob. 7.13PCh. 7.3 - Prob. 7.15PCh. 7.3 - Prob. 7.16PCh. 7.3 - Prob. 7.17PCh. 7.3 - Prob. 7.18PCh. 7.3 - Prob. 7.19PCh. 7.3 - Prob. 7.20PCh. 7.3 - Prob. 7.21PCh. 7.3 - Prob. 7.22PCh. 7.4 - Prob. 7.23PCh. 7.4 - Prob. 7.24PCh. 7.4 - Prob. 7.25PCh. 7.4 - Prob. 7.26PCh. 7.4 - Prob. 7.27PCh. 7.4 - Prob. 7.28PCh. 7.4 - Prob. 7.29PCh. 7.5 - Prob. 7.31PCh. 7.5 - Prob. 7.32PCh. 7 - Prob. 7.33PCh. 7 - Prob. 7.34PCh. 7 - Prob. 7.35PCh. 7 - Prob. 7.36PCh. 7 - Prob. 7.37PCh. 7 - Prob. 7.38PCh. 7 - Prob. 7.39PCh. 7 - Prob. 7.40PCh. 7 - Prob. 7.42PCh. 7 - Prob. 7.43PCh. 7 - Prob. 7.44PCh. 7 - Prob. 7.45PCh. 7 - Prob. 7.46PCh. 7 - Prob. 7.47PCh. 7 - Prob. 7.49PCh. 7 - Prob. 7.50PCh. 7 - Prob. 7.51PCh. 7 - Prob. 7.52PCh. 7 - Prob. 7.54PCh. 7 - Prob. 7.56PCh. 7 - Prob. 7.57P
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- If you double the width of a one-dimensional infinite potential well, (a) is the energy of the ground state of the trapped electron multiplied by 4, 2, , , or some other number? (b) Are the energies of the higher energy states multiplied by this factor or by some other factor, depending on their quantum number?arrow_forwardAn electron, trapped in a one-dimensional infinite potential well 250 pm wide, is in its ground state. How much energy must it absorb if it is to jump up to the state with n= 4?arrow_forwardA free electron has a kinetic energy 13.3eV and is incident on a potential energy barrier of U =32.1eV and width w =0.091nm. What is the probability for the electron to penetrate this barrier (in %)? Check the correct answer and show all workarrow_forward
- For a particle in a 1-dimensional infinitely deep box of length L, the normalized wave function or the 1st excited state can be written as: Ψ2(x) = {1/i(2L)1/2} ( eibx -e-ibx), where b = 2π/L. Give the full expression that you need to solve to determine the probalibity of finding the particle in the 1st third of the box. Simplify as much as possible but do not solve any integrals.arrow_forwardAn electron is trapped in a finite potential well that is deep enough to allow the electron to exist in a state with n= 4. How many points of (a) zero probability and (b) maximum probability does its matter wave have within the well?arrow_forwardAn electron having total energy E = 4.50 eV approaches a rectangular energy barrier with U = 5.00 eV and L = 950 pm as shown. Classically, the electron cannot pass through the barrier because E < U. Quantum- mechanically, however, the probability of tunneling is not zero. (a) Calculate this probability, which is the transmission coefficient. (b) To what value would the width L of the potential barrier have to be increased for the chance of an incident 4.50-eV electron tunneling through the barrier to be one in one million?arrow_forward
- Consider a potential energy barrierbut whose height Ub is 6.0 eV and whose thickness L is 0.70 nm.What is the energy of an incident electron whose transmissioncoefficient is 0.0010?arrow_forwardShow transcribed data (d) Find (r) and (r2) for an electron in a circular orbit of hydrogen with arbitrary prin- cipal quantum number n (corresponds to l = n - 1 and any allowed m). (e) Compute the RMS uncertainty ✓(r) – (r)2 in terms of r for the electron in part (d). Note that the fractional spread in r decreases with increasing n (in this sense the system "begins to look classical” for large n). How much more volume does a hydrogen atom in the n = 100 state occupy compared to the hydrogen atom in the ground state. (Hint - you might want to look at Griffiths 4.55, or 4.15 in the second edition)arrow_forwardProve that assuming n = 0 for a quantum particle in an infinitely deep potential well leads to a violation of the uncertainty principle Δpx Δx ≥ h/2.arrow_forward
- Whether the energy gap for a system decreases, is constant, or increases as the initial quantum number for the transition increases can be determined by calculating the second derivative of the energy level expression with respect to the quantum number. Calculate the second derivative with respect to the quantum number of the energy level expression for a linear rotor, EJ = hBJ(J+1) and also for the harmonic oscillator, Ev = hυ\upsilonυ(v+1/2).arrow_forwardFind the directions in space where the angular probability density for the l = 2, ml = 0 electron in hydrogen has its maxima and minima.arrow_forwardTwo identical particles of spin ½ are moving under the influence of a onedimensional harmonic oscillator potential. Assuming that the two-particle system is in a triplet spin state, find the energy levels, the wave functions, and the degeneracies corresponding to the three lowest states.arrow_forward
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