What's the name of the wavefxn int. showing normalizability?

  • Thread starter Zacarias Nason
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In summary, the expression on the LHS, \int_{-\infty}^{\infty}|\psi(x,t)|^2 dx = 1, is known as the squared norm of the L2 vector. It describes a pure quantum state in the wave mechanics of Erwin Schrödinger and represents the probability density of the particle. However, the wavefunction must be normalizable and square integrable for it to be considered a valid probability density.
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Zacarias Nason
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This is just a nomenclature thing; I'm aware that when dealing with the integral

[tex] \int_{-\infty}^{\infty}|\psi(x,t)|^2 dx = 1 [/tex]

that the integrand is the wavefunction, the wavefunction must be normalizable for it to be viewed as a probability density, it's referred to as the state of the particle, it needs to be square integrable, etc...but what is the name for this overall expression on the LHS, integral and all? I'm guessing it has a name and somewhere I missed it or lost it in my mind.
 
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  • #2
It is the squared norm of the L2 vector describing a pure quantum state in the wave mechanics of Erwin Schrödinger.
 
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Thank you!
 

1. What is a wavefunction?

A wavefunction is a mathematical representation of the quantum state of a system, which describes the probability of finding a particle at a certain position or momentum.

2. What does "normalizability" mean in relation to a wavefunction?

Normalizability refers to the property of a wavefunction where the total probability of finding a particle within a given space is equal to 1. This ensures that the wavefunction is physically meaningful and can accurately describe the behavior of a quantum system.

3. Why is it important for a wavefunction to be normalizable?

A wavefunction must be normalizable in order to accurately represent the behavior of a quantum system. If a wavefunction is not normalizable, it would mean that the probability of finding a particle in a certain space is infinite, which is not physically possible.

4. How do scientists determine if a wavefunction is normalizable?

To determine if a wavefunction is normalizable, scientists use mathematical techniques such as integration and the normalization condition (which states that the integral of the wavefunction squared over all space must equal 1).

5. Can a wavefunction ever be non-normalizable?

In certain cases, a wavefunction may be non-normalizable, such as for an infinite potential well or a free particle. However, in these cases, scientists can still use normalization techniques to define a normalized wavefunction that accurately describes the system.

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