# Normalization constant A of a harmonic oscillator

• Sorin2225
In summary, the conversation discusses the calculation of the modulus of a complex number and how it applies to the given equation. It is mentioned that the absolute value is not equal to the sum of the absolute values in general. The conversation also explores the concept of multiplying out the equation and determining the result.
Sorin2225
Homework Statement
Finding the normalization constant A of a harmonic oscillator
Relevant Equations
(psi(x,t))^2=1

I've worked through it doing what I thought I should have done. I normalized the original wavefunction(x,0) and made it = one before using orthonormality to get to A^2(1-1) because i^2=-1 but my final answer comes out at 1/0 which is undefined and I don't see how that could be correct since A is meant to be a real number. I'm not really sure where I've gone wrong either so any insight would be appreciated.

##\lvert \psi_1 + i \psi_4 \rvert^2 \ne (\psi_1 + i \psi_4)^2##

The vertical lines matter.

So it's the absolute value? which means that it's +1 not -1?

What is “it”?

|iψ4*iψ4|

That's not how absolute values work. You can't say ##\lvert a+b \rvert = \lvert a \rvert + \lvert b \rvert## in general.

How do you calculate the modulus of a complex number?

sqrt(a^2+b^2) so it would be Sqrt((i^2)^2+((psi(4)^2)^2))

##|\Psi|^2=\Psi^*\Psi=[A(\psi_1+i\psi_4)][A^*(\psi^*_1-i\psi^*_4)]##. What do you get when you multiply it out?

## 1. What is the significance of the normalization constant A in a harmonic oscillator?

The normalization constant A is a mathematical factor that ensures the wave function of a harmonic oscillator is properly normalized, meaning that the total probability of finding the particle in any location is equal to 1. It also helps to determine the amplitude and energy of the oscillator.

## 2. How is the normalization constant A calculated for a harmonic oscillator?

The normalization constant A is calculated by solving the integral of the square of the wave function over all space. This integral must equal 1 in order for the wave function to be properly normalized. The resulting equation is then solved for A.

## 3. What happens if the normalization constant A is not included in the wave function of a harmonic oscillator?

If the normalization constant A is not included, the wave function will not be properly normalized and will not accurately represent the probability of finding the particle in different locations. This can lead to incorrect predictions and results in calculations.

## 4. Can the normalization constant A change for different types of harmonic oscillators?

Yes, the normalization constant A can change for different types of harmonic oscillators. It is dependent on the specific wave function and potential energy of the oscillator. For example, the A value for a simple harmonic oscillator will be different from that of a quantum harmonic oscillator.

## 5. How does the normalization constant A affect the energy levels of a harmonic oscillator?

The normalization constant A is directly related to the energy levels of a harmonic oscillator. It is used to calculate the amplitude of the wave function, which in turn determines the energy levels. A larger A value will result in higher energy levels, while a smaller A value will result in lower energy levels.

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