by cragar
Tags: expectation, values
 P: 2,422 Is it possible to define operators to find the expectation value of position for a Gaussian wave packet. Similar to finding raising and lowering operators for the harmonic oscillator in terms of position and momentum and then using those to find and

. But I was just wondering if this could be done for a Gaussian wave packet.

 Mentor P: 9,634 Here is one: X If your wave packet is expressed as function of position, ## = \int \psi \psi^* x dx##.
 P: 2,422 I don't completely understand what you are doing? Is X my new operator. are you starting with the definition of expectation value and then going from there.
Mentor
P: 10,699

The position operator (in the position representation) is simply ##x##. So the general definition of expectation value:

$$\langle A \rangle = \int {\Psi^* A_{op} \Psi dx}$$

becomes

$$\langle x \rangle = \int {\Psi^* x \Psi dx}$$

Plug in your wave function and grind out the integral.
 P: 2,422 ok i understand that. I was trying to think of a way to compute that with out doing an integral. Like how you can do that for the harmonic oscillator with a+ and a - like $=$ u is the wave function and a+ is the raising operator. can I do this for a Gaussian wave packet.
 Mentor P: 9,634 If you define appropriate operators. For a gaussian wave packet, the expectation value of the position is the central value of the distribution. If you know that, you are done.

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