Solve Quantum Mech Problem: Find N for Normalized Wavefunction

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In summary, the conversation is about finding the value of N that will make the state |U> with Schrodinger position representation wavefunction U(x) = N exp(-((x-y)^2)/2a^2) normalized, where a and y are real constants. The person asking the question is also unsure of what "normalized" means and is asking for clarification.
  • #1
IanSimcox
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Hi, I'm not sure this is the correct topic for this question, but I shall ask anyway.

I've been set this question for homework and I'm not too sure where to start.

Find N so that the state |U> with Schrodinger position representation wavefunction U(x) = N exp(-((x-y)^2)/2a^2) is normalised, where a and y are real constants.

Hopefully from there I will be able to do the rest of the question.
 
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  • #2
Do you know what 'normalised' means? Look it up!
 
  • #3
Ok this could make me look like an idiot either way (probably coz I'm not too sure of what I'm about to say, I should listen more), but I think it means that if I integrate U(x) from -infinte to +infinite then the answer should be 1. If it is I feel kinda silly not havin thought of doing that.
 
  • #4
No,u have to integrate the square modulus...of the wave function.

Daniel.
 

Related to Solve Quantum Mech Problem: Find N for Normalized Wavefunction

1. What is a normalized wavefunction?

A normalized wavefunction is a mathematical function that describes the probability of finding a particle in a particular state in quantum mechanics. It is normalized if the integral of the square of the wavefunction over all space is equal to 1, which ensures that the total probability of finding the particle in any state is 100%.

2. Why is it important to solve for N in a normalized wavefunction?

Solving for N in a normalized wavefunction is important because it ensures that the wavefunction accurately describes the probability of finding a particle in a particular state. Without a properly normalized wavefunction, the probabilities calculated using the wavefunction will not be accurate.

3. How do you solve for N in a normalized wavefunction?

To solve for N in a normalized wavefunction, you must first square the wavefunction and then integrate it over all space. The resulting integral must then be set equal to 1 and solved for N. This will give you the value of N that will normalize the wavefunction.

4. What happens if the wavefunction is not normalized?

If the wavefunction is not normalized, the probabilities calculated using the wavefunction will not accurately represent the actual probabilities of finding a particle in a particular state. This can lead to incorrect predictions and results in quantum mechanics.

5. Can you have a wavefunction with negative values?

Yes, a wavefunction can have negative values. In quantum mechanics, the wavefunction is a complex number that includes both a real and imaginary part. The overall probability of finding a particle is determined by the square of the wavefunction, so the negative values will ultimately cancel out when calculating probabilities.

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