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classes:2009:fall:phys4101.001:q_a_1019 [2009/10/19 00:58] – x500_moore616classes:2009:fall:phys4101.001:q_a_1019 [2009/10/20 01:00] (current) – x500_santi026
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 <math> = 0? </math> <math> = 0? </math>
  
-because <math>\frac{d \Psi}{dx}</math> always goes to zero at infinity, and the derivative with respect to time of that would be zero?+because <math>\frac{d \Psi}{dx}</math> always goes to zero at infinity, and the derivative with respect to time of that would be zero?  I assume operators can operate on other operators, too, right?
  
 Why do you want to know, anyway? Why do you want to know, anyway?
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 == East End 10/19 12:30 am == == East End 10/19 12:30 am ==
 Actually, the way you describe is exactly how I solved the problem (the identity, the integration by parts, the terms going to zero, you name it).  That isn't exactly using intuition and approximations based on what's going on, which is what the exam hinted at.  I am curious about these intuitive methods and approximations.  Anybody else? Actually, the way you describe is exactly how I solved the problem (the identity, the integration by parts, the terms going to zero, you name it).  That isn't exactly using intuition and approximations based on what's going on, which is what the exam hinted at.  I am curious about these intuitive methods and approximations.  Anybody else?
 +
 +(Also, I disagree about the notecards.  I am pretty bad at memorizing mechanically usually, and think being able to write down things like the definition of a+/-, [a+,a-], etc, would be a nice, small, and reasonable help.  I personally think this is exactly what reference materials are for in the "real world," and think that we should be allowed a full-sized crib sheet.  For me, historically, creating a crib sheet is excellent review time, forcing me to review everything, and giving me the chance to realize what topics I don't understand fully and spend more time on those topics in my studying.)
  
 ====poit0009 10/18 12:20 PM==== ====poit0009 10/18 12:20 PM====
  
 In the problem with the two finite wells (2.47), the system could model a diatomic molecule sharing an electron.  In the ground state of the wave function, it is energetically favorable to have the wells closer together.  This means there is an attractive force while the electron is in the ground state.  Is there a repulsive force when the electron is in the first excited state? In the problem with the two finite wells (2.47), the system could model a diatomic molecule sharing an electron.  In the ground state of the wave function, it is energetically favorable to have the wells closer together.  This means there is an attractive force while the electron is in the ground state.  Is there a repulsive force when the electron is in the first excited state?
 +
 +=== Zeno 10/19 9AM ===
 +
 +Oddly, yes, that's exactly right. We know that Energy is proportional to frequency, which is inversely proportional to wavelength, which in discussion we determined is proportional to b for the first excited state; increasing the width between the wave crests increased its effective wavelength, decreasing its frequency and therefore reducing its energy, so Energy is inversely proportional to b for the first excited state. Since E minimizes as b-> infinity, the nuclei are pushed apart. For the even waveform, the ground state, the energy is lowest for b=0. The frequency is essentially zero and the wavelength is essentially infinite, making E essentially zero. For b>0, the 'dip' between the wave crests can be considered the valley of oscillation, resulting in an apparent wavelength and an increased frequency. In this case, as frequency increases Energy does as well, meaning that E increases with b. Since E is minimized at b=0, the ground state electron strives to pull the nuclei together. This is a very interesting problem conceptually, and serves as an introduction to the important anti intuitive results we obtain in studying Quantum Mechanics. I hope that explanation was clear and correct.
  
 ====Schrodinger's Dog 10/18 3:50PM==== ====Schrodinger's Dog 10/18 3:50PM====
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 Later in chapter 3, Griffths talks about how the free particle has a continuous spectrum k and how  infinite square well has a discrete spectrum n, but says that wavefunction of a continuous spectrum sometimes lie in Hilbert space, which makes our wavefunction unphysical. Could this be a reason why he said we didn't have a wavefunction which worked for the free particle in chapter 2?  Later in chapter 3, Griffths talks about how the free particle has a continuous spectrum k and how  infinite square well has a discrete spectrum n, but says that wavefunction of a continuous spectrum sometimes lie in Hilbert space, which makes our wavefunction unphysical. Could this be a reason why he said we didn't have a wavefunction which worked for the free particle in chapter 2? 
  
 +
 +====Captain America 10/19 10:33====
 +When dealing with all of these matrices and eigenvectors it is easy to lose track of what physical importance any of this is.  To break it down some, what exactly would it mean for something like problem 3.37, when "The Hamiltonian for a certain three-level system is represented by the matrix..."?  Is a three level system in this sense a system that has three possible states and we try to find them or is it a three particle system that has these particles in each of these three states?  
 +
 +Also does anyone have any quick hints on how to conceptualize the rest of this linear algebra better in terms of physics?
 +
 +====chavez 10/19 10:38====
 +Can someone explain the significance of the Axiom on page 102?
 +
 +===Captain America 10/19 11:05===
 +I believe this is similar to saying that any wavefunction can be described by the linear combination of certain other wavefunctions, as described by Fourier's theorem.  In this axiom, the eigenfunctions of an observable correspond to the wavefunctions of that observable, which as we have seen in the previous chapters can indeed be described by a combination of wavefunctions.
 +
 +====Esquire 10/19 1:21pm====
 +This question is not entirely pertinent to the current subject, yet it crossed my mind nonetheless. When working in the simple harmonic oscillator potential scenario, we found that energy values are increments of 1/2. Does this mean that only Fermions can be modeled with SHO?
 +
 +===chavez 10/19 6:12PM===
 +The simple harmonic oscillator has energy level increments of 1. <math>E_{n} = (n + \frac{1}{2})\hbar\omega</math>
 +
 +
 +=== Can 10/19 11:21pm ===
 +I thought I understood SHO,and just like chavaz said <math>E_{n} = (n + \frac{1}{2})\hbar\omega</math>, but now I am confused,  how do you make the jump from SHO to fermions?
 +
 +
 +=== ice IX 10/20 00:44 ===
 +You are thinking of spin 1/2 for fermions, which has nothing to do with the energy value increments for the SHO; any particle can be in such a potential.
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classes/2009/fall/phys4101.001/q_a_1019.1255931888.txt.gz · Last modified: 2009/10/19 00:58 by x500_moore616

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