Parth G | Nobody Knows Why Wave Functions Exist - So We Just Assume They Do (Quantum Mechanics Postulates) @ParthGChannel | Uploaded 2 years ago | Updated 16 hours ago
Wave functions are a big part of the current formulation of quantum mechanics. But why do they exist? Well currently nobody knows!
Every theory in physics is based on a set of assumptions, also known as axioms or postulates. In other words, we develop theories by first starting with a set of ideas that we assume are true. Then we apply some mathematics to these ideas and build the theory.
An example of this is the Kinetic Theory of Gases. This theory studies how gases should behave, and the assumptions it works off include the idea that a gas is made up of small, spherical particles, and that the total volume of these particles is much smaller than the volume of the container they are in.
What happens when these assumptions are not true for the real gas we are studying? Simple - the theory becomes less and less accurate at predicting how the real gas should behave.
The important point here though is that every theory is based on some assumptions / postulates / axioms. These can be thought of as the rules of the theory. In this video we take a look at the first postulate of the Copenhagen Interpretation of Quantum Mechanics.
The first postulate says that for any quantum system we're studying, there exists a mathematical quantity known as the wave function. The wave function is a quantity that has some value at every point in space and time. This value can be positive, negative, zero, or even imaginary.
When we take the square modulus of the wave function, we can find information about what we'd expect to see with the system, when we make a measurement on it. For example if our system is a single electron, the square modulus of its wave function can give us information about how likely we are to find the electron between different points in space.
Why is this the case? Nobody knows - quantum theory just seems to be based on this strange idea, and yet makes excellent predictions about how the world around us should behave. This is why we stick with the idea of wave functions in the first place. We don't understand quite why the universe behaves as if wave functions exist, but our mathematical formulation agrees very strongly with experimental data.
The wave function has to have some important properties. Firstly, it has to follow the Schrodinger Equation. This is the equation that determines how wave functions are allowed to evolve over time and through space.
Secondly, the area under the square modulus of the wave function directly corresponds to probabilities of experimental results when we make a measurement on the system - we've seen this idea already.
Thirdly, the wave function's square modulus has to be "normalizable". This means the total area under the square modulus has to be finite, and we must be able to set this area to 1. This is because this total area gives us the probability of finding the electron SOMEWHERE in our universe, and this must be 100% = 1.
Many of you have asked about the stuff I use to make my videos, so I'm posting some affiliate links here! I make a small commission if you make a purchase through these links.
A Quantum Physics Book I Enjoy: https://amzn.to/3sxLlgL
My Camera (Sony A6400): https://amzn.to/2SjZzWq
ND Filter: https://amzn.to/3qoGwHk
Microphone and Stand (Fifine): https://amzn.to/2OwyWvt
Gorillapod Tripod: https://amzn.to/3wQ0L2Q
Thanks so much for watching - please do check out my socials here:
Instagram - @parthvlogs
Patreon - patreon.com/parthg
Music Chanel - Parth G's Shenanigans
Merch - https://parth-gs-merch-stand.creator-spring.com/
Timestamps:
0:00 - Theories in Physics, and the Assumptions They are Based on
0:57 - Postulates in the Kinetic Theory of Gases
2:20 - The First Postulate of (the Copenhagen Interpretation of) Quantum Mechanics
3:35 - How Does a Wave Function Relate to a Real System? Probability Densities
5:33 - WHY Does a Wave Function Even Exist? Why Do We Use the Wave Function?
7:06 - Properties of the Wave Function
8:32 - Thanks for Watching, Please Check Out my Quantum Merch in the Description!
Wave functions are a big part of the current formulation of quantum mechanics. But why do they exist? Well currently nobody knows!
Every theory in physics is based on a set of assumptions, also known as axioms or postulates. In other words, we develop theories by first starting with a set of ideas that we assume are true. Then we apply some mathematics to these ideas and build the theory.
An example of this is the Kinetic Theory of Gases. This theory studies how gases should behave, and the assumptions it works off include the idea that a gas is made up of small, spherical particles, and that the total volume of these particles is much smaller than the volume of the container they are in.
What happens when these assumptions are not true for the real gas we are studying? Simple - the theory becomes less and less accurate at predicting how the real gas should behave.
The important point here though is that every theory is based on some assumptions / postulates / axioms. These can be thought of as the rules of the theory. In this video we take a look at the first postulate of the Copenhagen Interpretation of Quantum Mechanics.
The first postulate says that for any quantum system we're studying, there exists a mathematical quantity known as the wave function. The wave function is a quantity that has some value at every point in space and time. This value can be positive, negative, zero, or even imaginary.
When we take the square modulus of the wave function, we can find information about what we'd expect to see with the system, when we make a measurement on it. For example if our system is a single electron, the square modulus of its wave function can give us information about how likely we are to find the electron between different points in space.
Why is this the case? Nobody knows - quantum theory just seems to be based on this strange idea, and yet makes excellent predictions about how the world around us should behave. This is why we stick with the idea of wave functions in the first place. We don't understand quite why the universe behaves as if wave functions exist, but our mathematical formulation agrees very strongly with experimental data.
The wave function has to have some important properties. Firstly, it has to follow the Schrodinger Equation. This is the equation that determines how wave functions are allowed to evolve over time and through space.
Secondly, the area under the square modulus of the wave function directly corresponds to probabilities of experimental results when we make a measurement on the system - we've seen this idea already.
Thirdly, the wave function's square modulus has to be "normalizable". This means the total area under the square modulus has to be finite, and we must be able to set this area to 1. This is because this total area gives us the probability of finding the electron SOMEWHERE in our universe, and this must be 100% = 1.
Many of you have asked about the stuff I use to make my videos, so I'm posting some affiliate links here! I make a small commission if you make a purchase through these links.
A Quantum Physics Book I Enjoy: https://amzn.to/3sxLlgL
My Camera (Sony A6400): https://amzn.to/2SjZzWq
ND Filter: https://amzn.to/3qoGwHk
Microphone and Stand (Fifine): https://amzn.to/2OwyWvt
Gorillapod Tripod: https://amzn.to/3wQ0L2Q
Thanks so much for watching - please do check out my socials here:
Instagram - @parthvlogs
Patreon - patreon.com/parthg
Music Chanel - Parth G's Shenanigans
Merch - https://parth-gs-merch-stand.creator-spring.com/
Timestamps:
0:00 - Theories in Physics, and the Assumptions They are Based on
0:57 - Postulates in the Kinetic Theory of Gases
2:20 - The First Postulate of (the Copenhagen Interpretation of) Quantum Mechanics
3:35 - How Does a Wave Function Relate to a Real System? Probability Densities
5:33 - WHY Does a Wave Function Even Exist? Why Do We Use the Wave Function?
7:06 - Properties of the Wave Function
8:32 - Thanks for Watching, Please Check Out my Quantum Merch in the Description!
