Ground state of harmonic oscillator

  • Thread starter Knot Head
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  • #1
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Homework Statement


Verify that the ground state (n=0) wavefunction is an eigenstate of the harmonic
oscillator Hamiltonian. Using the explicit wavefunction of the ground state to calculate
the average potential energy <0|[tex]\hat{v}[/tex]|0> and average kinetic energy <0|[tex]\hat{T}[/tex]| 0>


Homework Equations



[tex]\int^{\infty}_{0}[/tex](x[tex]^{2n}[/tex] e[tex]^{-ax^{2}}[/tex])dx=[tex]\frac{1x3x5x...x(2n-1)}{2^(n+1)a^n}[/tex][tex]\sqrt{\frac{\pi}{a}}[/tex]


The Attempt at a Solution


I did the ground state harmonic oscillation standard alteration with "a" and got [tex]\\Psi_{0}[/tex](x)=1/([tex]\pi^{1/4}[/tex][tex]\sqrt{x_{0}}[/tex])*e^-x^2/2x[tex]^{2}_{0}[/tex]
 

Answers and Replies

  • #2
vela
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You're going to have to make a bit more of an effort to work the problem on your own before you'll get any help here.
 
  • #3
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ill just go ask this question another website, thanx
 

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