Professor Dave again, let’s take a look at the Schrodinger equation. Through the work of Planck and Einstein we were forced to accept that energy is quantized, and that light exhibits wave particle duality. Then, de Broglie extended this duality to include matter as well, meaning that all matter has a wavelength, from a tiny electron, to your whole body, to a massive star. However, an object’s wavelength is inversely proportional to its mass, so objects bigger than a molecule have a wavelength that is so tiny that it is completely negligible. But an electron is incredibly small, so small that its wavelength is indeed relevant, being around the size of an atom, so we must view electrons as both particles and waves from now on. Therefore, we must discuss the wave nature of the electron. So what kind of wave might this be? We can regard an electron in an atom as a standing wave, just like the kind we learned about in classical physics, except that rather than something like a plucked guitar string, an electron is a circular standing wave surrounding the nucleus. If we understand this, it becomes immediately apparent why quantization of energy applies to the electron, because any circular standing wave must have an integer number of wavelengths in order to exist. Given that an increasing number of wavelengths means more energy carried by the wave, we can see the Bohr model for the hydrogen atom begin to emerge as we imagine a standing wave with one wavelength, and then two, and then three and so forth. This is the reason that an electron in an atom can only inhabit a discrete set of energy levels, the circular standing wave that represents the electron can only have an integer number of wavelengths. When an electron is struck by a photon of a particular energy, this energy is absorbed, promoting the electron to a higher energy state and increasing the number of wavelengths contained within the standing wave. This is why the electron goes to inhabit a higher energy level, and this is what is fundamentally occurring during electron excitation. Furthermore, it is the constructive interference of these standing waves that explains how orbital overlap results in covalent bonding, so we can enjoy a little more clarity in our understanding of chemistry thanks to modern physics. Once it was realized that electrons exhibit wave behavior, the physics community set out to find a mathematical model that could describe this behavior. Erwin Schrodinger achieved this goal in 1925 when he developed his Schrodinger equation, which incorporated the de Broglie relation. This is a differential equation which utilizes concepts in mathematics that are beyond the scope of this series, but we can certainly discuss the conceptual implications of the equation. Essentially, just as F=ma applies to Newtonian systems, the Schrodinger equation applies to quantum systems, by describing the system’s three-dimensional wave function represented by the Greek letter, psi. In this equation, this term is called the Hamiltonian operator, which is a set of mathematical operations that describes all the interactions that are affecting the state of the system, which can be interpreted as the total energy of a particle. But while the Schrodinger equation can calculate the wave function of a system, it does not specifically reveal what the wave function is. Max Born proposed that we interpret the wave function as a probability amplitude, where the square of the magnitude of the wave function describes the probability of an electron existing in a particular location. Looking back at the double slit experiment, we understand the diffraction pattern as illustrating this wave of probability. The pattern is not the electron itself, it is the probability that an electron will arrive at each location on the screen. We can’t predict where one electron will go, only the probability that it will arrive at a particular location. If many electrons arrive at the screen, it becomes apparent how their distribution obeys the wave function. So the Schrodinger equation does compute the wave function deterministically, but what the wave function tells us is probabilistic in nature. This idea that nature is probabilistic on the most fundamental level was a lot for the scientific community to handle at the time, and still is for some. So just the way sound waves are mechanical waves, and light waves are oscillations in an electromagnetic field, an electron can be considered a cloud of probability density. There are many such interpretations of quantum mechanics which involve different ways of viewing the relationship between the wave function, experimental results, and the nature of reality, and there is still no firm consensus as to which view is correct, be it the Copenhagen interpretation, many-worlds interpretation, or a number of others. But before you choose a camp, let’s keep moving through the development of quantum mechanics, which means we will need to consult Werner Heisenberg. Thanks for watching, guys. Subscribe to my channel for more tutorials, support me on patreon so I can keep making content, and as always feel free to email me:

are electrons themselves wavefunctions?

@ 5:47 "Before you choose a camp"

Comment: There is a book about scientific revolutions which claims new understandings in science often come about not because everyone agrees, but that older scientists pass away, and now the new understanding can proceed. This impeding seems to be choosing a camp. There is another explanation.

In doing anything, limited resources of time, materials, people, etc. must be allocated. Decisions need to be made. Someone might decide that a new explanation has not been sufficiently researched and not worthy, or be a Not Invented Here (NIH) person. Either way, science has limitations similar to other endeavors: limited resources.

Omg this was such a clear explanation. Thank you for saving my Pchem grade!

Why does electron revolve around the nucleus..

it is averrrrry good chaneel , but can you speak more slowely ? :'(

Can I ask a question please? Does the electron exist always in a single radius away from the atom, and the standing waves inside the same circumference? Does does it get further from the atom as well to fit the other standing waves? What I mean is, if you consider a single circumference, you can fit various standing waves of various energies there. But the electron could also be at a different distance and also fit different standing waves there. What I mean is, for different numbers of wavelengths, does the electron jump further away from the atom, or does it stay there and just fit more wavelengths into the smaller circumference?

so it is a probability wave or a standing wave ? also when electrons moving through space do they move also like particles and standing waves?

Professor, I want to see you in short hair. 🙀

Uhhhhh…srry, I’m 13

Excellent

Can you explain Einstein field equation

But what why shorter wavelength means smaller energy? The shorter the wavelength, the higher the frequency is, so doesn't it mean higher energy? Also, I've found this website where the wavelength-energy relationship looks opposite: http://sci.esa.int/education/50379-high-energy-wavelengths/

Love and Respect from Bangladesh……….

Your great sir

Bohemian mechanics is not an interpretation of QM.

Thank you so much for this video!

Why do we need a double slit to exhibit wave like nature of electron, why can't we have single slit to exhibit wave like nature of electron? It is inherent in quantum mechanic that wave like nature of a particle cannot exhibit its wave like nature by itself? It needs a corresponding particle to exhibit wave like nature?

Love the analogies and annotations as the pictures and visual aids change,providing clarity about a very messy,conceptually complex equation

This is the future of education.

i'd be happy if public schools let teachers put these type of vids instead of backwards boring vids that pass the time and are hard to follow.

The colour coding has helped everything sink in.

wtf im in 9th grade i came cuz i was bored but im gonna kill myself now

increasing wavelengths or frequencies ?????Sir….

I learned a lot. Thanks <3

hello sir please explain nanoelectronics

Very well explained…thank you

thanku Sir…

Hey professor, you look like #Ranveer_kapoor….. A Bollywood actor… seriously

Thank you

I’m not happy with the Schrodinger’s cat thought experiment and the concept of superposition in QM.

Thank you so much sir

1:37

Given that increasing number of wavelengths means more energy carried by the waves….."Are you sure?????? DECREASING wavelength (i.e. increasing frequency) means more energy carried by the electrons. "Wavelength" and "number of waves" are inversely proportional.

@Professor Dave explains. Can you explain Infinite squre well example of Qantum mschanics.

you should be paid not my teacher

Salute to you

From india

Praveen kumar pathak

"forced to accept" is a logical fallacy. It is a black swan problem. Just because you cannot imagine black swans and have never seen them doesn't mean they don't exist. The whole mess of QM is based on not understanding how to think rationally. Schrodinger himself proved through logic the foundations of QM cannot be correct by definition.

When Jesus spawns again to save you from failing!

Why is this not just tautology?

Surely what you describe is an electron in a closed orbit. Without gaining/losing energy it stays there, much like a planet orbiting a star, but in the case of a planet the in/decrements are in infinitesimal quanta as the odd atom falls in or off.

Not de broleeh, de broy

It's pronounced as de bro-liye whaa

Pehli baar dekh mujhe hi esa laga ya kisi aur ko b ki ye Ranveer Kapoor hai bol k…

Ranveer Kapoor ka koi new advertisement😂😂 hoga socha tha thumbnail dekh😂😂

Jab play kiya tab pata chala ki ye toh koi aur hai 😂😂

"Einstien didnt liked quantum mechanics…!" 🙂

I am not a flat-earther but if notions of probability pretend to separate causes from effects I am a flat-earth Dutchman.

I also think that anomalies to conventional understanding always have the possibility of being coherently explained in relation to matter which is satisfactorily explained conventionally by means of a better general scheme of understanding – like using a tetrahedron as a basis for plotting space instead of a cube.

Hallelujah! Jesus Christ

What does the | mean in the equation? I mean I see that | seperates H(t) and phi, but I don't know what it means.

Ranbir Kapoor???

You are great sir

I have a question that if electron behaves like a wave then how can it called be a particle it must be a cloud of energy

But according to Standard model of elementary particles it is a particle

Can you help me I am in high school in India and don't mind it's my mom's ID

thank you pro❤

1:35

I don’t understand the diagram, as the energy levels (n) increase, the electron should move farther away from the nucleus (in accord with bohr’s model) but here, the wavelength stays in one position, why so?

( I’m probably wrong so don’t judge)

As a physics major, this is one of the best explanations of wave particle duality I have come across, and while I havn't actually messed around with the schrodinger equation yet, i have done the double slit experiment, worked with standing wave equations, ect. This is brilliantly concise and amazingly informative. Thank you sir.

About a year ago I dove deeply in quantum mechanics, almost as a hobby. Determined to understand the significance of the finding the Higgs-Boson particle, and why the construction of the LHC at CERN, led me into the depths of quantum mechanics. Not once in the dozens of hours I spent reading about quantum mechanics did I see the simplicity of the standing wave of an electron, and its relationship to the Schrodinger equation, like I just saw in less than 7 minutes. Thank you for taking the time and making the effort Prof. Dave!

Shit i got exams on Wednesday and I am watching videos on Quantum Mechanics today at Monday night

no word to mention your IQ level

You would look better with a shave, haircut, and a tucked shirt.

did he just say DIE Fraction? 4:24

You literally blew my mind with the part about electrons being described as standing waves. That one statement connected so many separate ideas in my head, including stuff from chemistry which I thought I'd never need to understand since I'm studying physics. This is a fantastic series, keep up the great work

It's not true that Einstein didn't like quantum mechanics (which by the way he helped to creat) , he simply didn't agree with some implication of the theory because he thought it was incomplete.

The icon picture looks like Ranbir Kapoor.

This is the best conceptual explanation of orbitals so far. Have always struggled with the idea of excitation of electrons but now this makes a lot more sense!!

The solutions to Schrodinger's equations are wave functions. Wave function really exist even though we can't measure them directly. They are configured by the physics constants to be able to express energy and momentum in specified ways.

Nice

sor I want to have video on quantum field theory

Woow thanks Prof Dave. May I ask if you have a PowerPoint presentation about this topic ? Thank you ❤️

Who knew Chris D'elia is such a smarty pants!

Sir at 2:43 you said that the constructive interference of theses orbitals with photon(external) results in and explain covalent bonding

Sir can you explain how?

وصف رائع thank you 😍

Why is it that when I Google Schrodinger's equation it looks different to these equations presented here? Can anyone explain?

thank you professor Dave sir.

OK but did not delve into the S Eq

What gives? I just now received this😐

Thanks a lot sir

I see the light … err … particle … err …

oh dave, makes a lot of sense man thanks

No cat jokes?

Thank you Ranbir kapoor

Excellent ! Tks

Best

I feel as if he's talking like BRIELLE from the Ellen show

Incredible concise explanation of QM. Took me months to understand this in undergrad.

Is the wave shape of an electron wave a sphere or a 2 d circle?

Can u explain scalar diffraction theory in Fourier optics

Increased number wavelength means decreased energy right? E=h×c÷(wavelength)

I think wavefunctions describe the the only thing that does exist.

I'm too high for this

this is too much for me,

however, if anyone care to clarify this, it will be very appreciated,

is Copenhagen interpretation the same with spontaneous collapse interpretation?

This vid is in my syllabus

modern aristotle of this time

this video help me with a high school assessment

👏

Is it a first-order PDE? How many independent variables? I'm just starting this stuff so don't everyone pile on.

F*** this guy. You alone know everything in this world. Why???!!!😂😂😂

you are the best thank you

I've got a headache

I wish to add Arabic subtitles in your videos

Your explanation is very beautiful and simplifies information

Video is 6 minutes, 28 seconds long.

Seems suspicious …

Oh well, probably nothing. Hey, anyone want pie? I have two.

This might be God, It looks like jesus to me.

but the Schrodinger equation is totally incompatible with Einsteins relativity and it also doesn't account for the internal properties of electrons such as the quantum spin….so for fast moving electrons and electrons in electromagnetic field Schrodinger eq gives the wrong answers

that's why Paul Dirac solved this problem with his Dirac equation, a fully relativistic equation….

Beautifully Done!

The goat

Thanks

Im a freshman majoring in bme at washu and these videos are incredibly helpful

You deserve a lot of likes,views and subscribers……