Expectation value of total energy

  • Thread starter Chronos000
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  • #1
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Homework Statement



given a wavefuntion [tex]\Psi[/tex] = (1/sqrt50) (3[tex]\mu[/tex]1 + 5[tex]\mu[/tex]2 - 4[tex]\mu[/tex]3)

what is the expectation value of the total energy?


My thoughts were to calculate <[tex]\Psi[/tex]|[tex]\hat{}H[/tex]|[tex]\Psi[/tex]>

but the previous part to the question asks for the probability of each outcome(which I know how to find). So is there a way to do this using the probabilities?
 

Answers and Replies

  • #2
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For a discrete probability distribution [tex]f(x_i)[/tex] [x (and thus f) takes only discrete values], the expectation value of a quantity [tex]x[/tex] is

[tex]<x>= \sum^N_i x_i f(x_i) [/tex],

where x takes on values [tex]x_1, x_2, \ldots , x_N[/tex]

For a continous probability distribution [tex]g(x)[/tex] [where g and x are continous], the expectation value of x is the limit of the sum, namely the integral

[tex]<x>= \int^{x_{max}}_{x_{min}} x g(x) [/tex].

So if you know the probability distribution (which it seems like you do) the rest is basic maths.
 
  • #3
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so are you saying that the answer is just ET = 9/50 E1 + 25/50 E2 + 16/50 E3 ?
 
  • #4
ideasrule
Homework Helper
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Yes.
 

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