ANY HELP IS MUCH APPRECIATED, I ALWAYS RATE, THANKS!!! . Complex functions in th

Question

ANY HELP IS MUCH APPRECIATED, I ALWAYS RATE, THANKS!!! . Complex functions in the form eikx can be used tomodel the wavefunctions of particles in a linear accelerator. Showthat any linear combination of the complex functionse2ix and e-2ix is an eigenfunction of theoperator d2/dx2 and identify itseigenvalue. . ANY HELP IS MUCH APPRECIATED, I ALWAYS RATE, THANKS!!! . Complex functions in the form eikx can be used tomodel the wavefunctions of particles in a linear accelerator. Showthat any linear combination of the complex functionse2ix and e-2ix is an eigenfunction of theoperator d2/dx2 and identify itseigenvalue. .

Explanation / Answer

let = A*exp(2ix) + B*exp(-2ix) is an eigenfunction if d2/dx2 =a* , where a is some constant d2/dx2 [ A*exp(2ix) + B*exp(-2ix)] =2i*2i*A*exp(2ix) + (-2i)*(-2i)*B*exp(2ix) = -4*A*exp(2ix) - 4*B*exp(-2ix) = -4*[A*exp(2ix) + B*exp(-2ix) ] = -4* eigenvalue is -4

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---