Understanding Wavefunctions and Normalization: Exploring Solutions in PChem

In summary, the conversation is about a person seeking help with understanding wavefunctions in their pchem class. The problem involves normalizing an unnormalized wavefunction and the person knows the answer is N = sqrt(1/2pi). However, they are stuck at the step of integrating e^(-iψ)* e(iψ) dψ and determining the value of N.
  • #1
tbair200
1
0
Please I need help with wavefunctions!

Okay so I have attempted to understand wavefunctions in my pchem class but I am a little lost... Here is the problem.
unnormalized wavefunction (ψ) = e^(iψ) with 0≤ψ≤2∏, normalize this equation

Homework Equations



N^2∫ (ψ)^2 dψ

**I uploaded a pic of relevant equations bc it would be too messy to write out on here



The Attempt at a Solution



Okay so I know the answer is N = sqrt (1/2pi)

but I get to this step...

N^2 ∫ e^(-iψ)* e(iψ) dψ

and I am not sure where to go from here... I know ψ^2 = 1 but I am still stuck
 

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  • #2


tbair200 said:
Okay so I have attempted to understand wavefunctions in my pchem class but I am a little lost... Here is the problem.
unnormalized wavefunction (ψ) = e^(iψ) with 0≤ψ≤2∏, normalize this equation

Homework Equations



N^2∫ (ψ)^2 dψ

**I uploaded a pic of relevant equations bc it would be too messy to write out on here



The Attempt at a Solution



Okay so I know the answer is N = sqrt (1/2pi)

but I get to this step...

N^2 ∫ e^(-iψ)* e(iψ) dψ

and I am not sure where to go from here... I know ψ^2 = 1 but I am still stuck

Not sure why you are stuck. The integral of 1 from 0 to 2pi is 2pi. So N^2*(2pi)=1. What's N?
 

FAQ: Understanding Wavefunctions and Normalization: Exploring Solutions in PChem

What are wavefunctions?

Wavefunctions are mathematical descriptions of the quantum state of a physical system. They contain information about the position, momentum, and other properties of particles in the system.

Why are wavefunctions important?

Wavefunctions are important because they play a crucial role in understanding and predicting the behavior of quantum systems. They are used in various fields such as quantum mechanics, quantum chemistry, and solid-state physics.

How are wavefunctions represented?

Wavefunctions are typically represented by complex-valued functions, with the absolute square of the function representing the probability of finding a particle at a particular point in space.

What is the Schrödinger equation?

The Schrödinger equation is a fundamental equation in quantum mechanics that describes how the wavefunction of a quantum system evolves over time. It relates the energy of a system to the wavefunction and allows us to make predictions about the behavior of particles in the system.

How do wavefunctions relate to the uncertainty principle?

Wavefunctions are closely related to the uncertainty principle, which states that it is impossible to know both the position and momentum of a particle with absolute certainty. The wavefunction describes the probability of a particle having a certain position and momentum, and the uncertainty principle places limits on how accurately these properties can be known simultaneously.

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