• Homework 1: (Due Monday, September 28)   

  This first homework is to test your knowledge of basic calculus which will be needed throughout this course.
  It is intended to give you an idea about how well your math background is in relation to this course.
  If you are experiencing major problems in carrying out these operations, then you have defficiencies in the knowledge
  prerequisite to this course. Chances are you will have trouble in following this course, and will not be able to 
  perform well in the exams. I suggest you do a quick review of the relevant material.
  

  First Homework

• Homework 2: (Due Monday, Oct 5)

  Given the wavefunction of a particle at time t=0:
  
    Ψ(x,0) = A x exp[-(x/xo)2 + ikox]
    
  Find the following quantities:
  
  (a) The normalization constant A.
  
  (b) < x >
  
  (c) < x2 >
  
  (d) < p >
  
  (e) < p2 >
  
  (f) Δx Δp
  
  
  

• Homework 3: (Due Wednesday, October 14)
  A particle in a one -dimensional infinite square-box potential of width \(a\) is known to be in the state
  \(\Psi(x,0) = A [3u_1(x) + 4u_3(x)] \) at time \(t=0\). The functions \(u_n\) are the eigenstates of the system.
  Find
  • the normalization constant \(A\),
  • \( \Psi(x,t) \),
  • <\(x\)>\((t)\),
  • <\(x^2\)>\((t)\).
  How would you qualitatively describe the development of the wavefunction?

• Homework 4: (Due Monday, October 26)
  Consider the wavefunction \( \Psi(x)=A \exp[-(x/x_o)^2 +ik_ox]\).
  • Obtain the momentum-space wavefunction \(g(k)\).
  • Find the expectation value <\(p\)> using \(g(k)\).
  • Find the expectation value <\(p^2\)> using \(g(k)\).

Each homework is to be placed as a single PDF document (which may contain photos of your work) and submitted through moodle.
Please name the file in the format:

Check the Stars system for your homework grade. In some cases, you may be able to re-submit your homework to the assistant with corrections and improve your grade.