College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Show that ? (x,t) = A cos (kx - ?t) is not a solution to the time-dependent Schroedinger equation for a free particle [U(x) = 0].
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- Show that the probability associated with the state Ψn for a particle in a one- dimensional box 0≤ x≤ L obeys the following relationship: (You can see the picture attached for the problem)arrow_forwardSolve the time-independent Schrödinger equation and determine the energy levels and the wave function of a particle in the potential a? V (x) = Vol a + 2r2 with a = const.arrow_forwardAn electron is trapped in an infinitely deep one-dimensional well of width 10 nm. Initially, the electron occupies the n = 4 state. Calculate the photon energy required to excite the electron in the ground state to the first excited state.arrow_forward
- Evaluate the E expressions for both the Classical (continuous, involves integration) and the Quantum (discrete, involves summation) models for the energy density u, (v).arrow_forwarda) Show that if the total energy ε of a single particle state can be written as the sum of independent energies EiA, εiB, εic... then its partition function will factorise into a product of partition functions ZAZBZC. b) Given the factorisation, show how the free energy F and quantities such as S and Cy can be expressed as a sum of terms dependent on the sources A, B, C.arrow_forwardConsider a weakly anharmonic a 1D oscillator with the poten- tial energy m U(x) = w?a² + Ba* 2 Calculate the energy levels in the first order in the small anharmonicity parameter 3 using TIPT and the ladder operators.arrow_forward
- A particle is in a three-dimensional cubical box that has side length L. For the state nX = 3, nY = 2, and nZ = 1, for what planes (in addition to the walls of the box) is the probability distribution function zero?arrow_forwardconsider an infinite square well with sides at x= -L/2 and x = L/2 (centered at the origin). Then the potential energy is 0 for [x] L/2 Let E be the total energy of the particle. =0 (a) Solve the one-dimensional time-independent Schrodinger equation to find y(x) in each region. (b) Apply the boundary condition that must be continuous. (c) Apply the normalization condition. (d) Find the allowed values of E. (e) Sketch w(x) for the three lowest energy states. (f) Compare your results for (d) and (e) to the infinite square well (with sides at x=0 and x=L)arrow_forwardProve in the canonical ensemble that, as T ! 0, the microstate probability ℘m approaches a constant for any ground state m with lowest energy E0 but is otherwise zero for Em > E0 . What is the constant?arrow_forward
- We have a three dimensional vector space where |P1), |P2) and |23) form a complete orthonormal basis. In this vector space we have two states |a)=5i|1)+3i 2)+(-2+2i) 3) and |B) =4i|1)-5 i) Calculate (a and (B, in terms of the dual basis vectors (y|, (p2|, (P3|. ii) Calculate the inner/scalar products (alB) and (Ba). Show that (8|a) =(a|B)".arrow_forwardThe wave function of a particle at time t= 0 is given by w(0) = (4,) +|u2})), where |u,) and u,) the normalized eigenstates with eigenvalues E and E, are respectively, (E, > E, ). The shortest time after which y(t) will become orthogonal to |w(0)) is - ħn (а) 2(E, – E,) (b) E, - E, (c) E, - E, (d) E, - E,arrow_forward
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