# What is the equation for the hypothetical wavefunction with a peak at z=1?

• Ruddiger27
In summary, the conversation discusses the equation for a wavefunction of a particle confined in a specific region of space and how to incorporate it into the equations for expectation values. The wavefunction is defined in a piecewise manner and the integral needs to be broken up into four regions to accurately represent the function.
Ruddiger27
Sorry, another quick question. If I have a particle confined in a region of space -4 <= Z <=6 where
psi(x)= A(4+z), -4<= z <=1
A(6-z), 1<= z <=6
0 , everywhere else

And I sketch the wavefunction based on the above definitions, what is the actual equation for the wavefunction? The graph gives a peak at z=1 and slopes down to zero either side. Is this supposed to represent a sin(x) function, or am I supposed to just take the above definitions and fit them into the equations for expectation values? I don't think these equations would work in the equation for expectation values.

That *is* the equation for the wavefunction... it is just defined in a piecewise manner. You need to take this definition and put it into the equations for expectation values... but you need to break up the integral into several regions, and put the particular piece of this wave function in. So instead of one integral from negative infinity to positive infinity, you'd have four integrals: negative infinity to -4 (psi is 0), -4 to 1 (psi is A(4+z)), 1 to 6 (psi is A(6-z)) and 6 to infinity (psi is 0 again).

Thanks, that's what I did, but it just seemed a bit wrong to me. Maybe because I thought there was more to it. Anyway, thank you.

## What is a hypothetical wavefunction?

A hypothetical wavefunction is a mathematical function used in quantum mechanics to describe the probability of finding a particle in a particular state.

## How is a hypothetical wavefunction different from a real wavefunction?

A hypothetical wavefunction is a theoretical concept and does not necessarily correspond to any physical system, while a real wavefunction describes the actual state of a physical system.

## What is the significance of a hypothetical wavefunction?

A hypothetical wavefunction allows us to make predictions about the behavior of quantum particles and understand their properties, such as energy and momentum.

## Can a hypothetical wavefunction be observed or measured?

No, a hypothetical wavefunction cannot be directly observed or measured. It is a mathematical tool used to make predictions about the behavior of quantum particles.

## How is a hypothetical wavefunction related to the Schrödinger equation?

The Schrödinger equation is used to calculate the evolution of a wavefunction over time, and a hypothetical wavefunction is one possible solution to this equation.

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