Born's Statistical (Probabilistic) Interpretation of Quantum Mechanics

Born's Statistical Interpretation, a fundamental concept in quantum mechanics, states that the square of the wave function's magnitude at any point gives the probability density of finding a particle at that point.
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Born's statistical interpretation is a cornerstone in the field of quantum mechanics, introduced by physicist Max Born in the 1920s. This interpretation fundamentally changed our understanding of quantum phenomena. In classical physics, the behavior and properties of physical systems are determined precisely. However, quantum mechanics, dealing with subatomic particles, exhibits inherent uncertainties.

Born's interpretation addresses the wave function, a key mathematical entity in quantum mechanics. The wave function, denoted usually as Ψ, describes the quantum state of a particle or system of particles. However, unlike classical equations that directly describe physical quantities, the wave function itself doesn't have a straightforward physical interpretation.

Born proposed that the square of the absolute value of the wave function, |Ψ|^2, should be understood as a probability density. In essence, the wave function provides a probabilistic framework for understanding quantum phenomena. This interpretation allowed for the calculation of probabilities of different outcomes in quantum experiments, where exact predictions are fundamentally impossible. It marked a significant shift from deterministic nature of Classical physics to In-deterministic or PROBABILISTIC nature of Quantum physics.

00:00 Introduction
01:41 Wavefunction & Schrodinger Equation
07:40 Born Statistical Interpretation
15:49 Max Born's Inspiration
20:29 Double Slit Experiment

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[dheeraj_matics]

If there will be unlimited like option in YouTube, I would not restrict my self to it for this video. Thanks a lot❤

[deepikadiwan]

Throughout the playlist you have been patiently and compassionately unfolding the mysterious layers of quantum word, it's more thrilling than any movie fir me. Thankyou so much

[zzzoldik]

You said the function tell about probability to find particle but I have heard for interpretating double slit that particle through both slit together in one time. This source from UNSW, they said that even single particle can get constructive interference with it self.

[khuebner]

Well done. Your lecture is very informative, pacing excellent, and math format is superb. Thank you

[KipIngram]

I want to give you some major kudos for really underscoring the proper interpretation of what the wave function is telling us about FUTURE measurements. Earlier on in the video I was worried you were going to do the oh so common "particle is in many places at once" thing, which I absolutely hate, but you dodged that bullet quite nicely. I love how you said very clearly that it's not THE PARTICLE that's "partially here, partially there, etc." but rather the probability of later finding the particle here or there. Very nice. I adhere to Feynman's wisdom on this - that we really should not talk about the values of things we have not yet measured as actually existing before we do so.

[harshsingh]

Respected sir, I love this series, to a point where I've made notes of every single lecture. As this is the only series which I could understand. It's my humble request to just be a little more consistent with it, perhaps a lecture every week. Thank you!

[岡安一壽-gy]

The important things about quantum mechanics are explained in an easy-to-understand way.
The notes on the board are easy to read. And the diagrams are beautiful.
By the way, surprisingly and unfortunately, most physicists believe that when two essentially indistinguishable coins are tossed, the probability of getting
①Both heads
②One head and one tail
③Both tails
are all 1/3.

Let's think about next question.

[Question]
Find the probabilities that the following events will occur when two dice are rolled.
①Both show odd numbers
②One shows odd number and another shows evenn number
③Both show even number

P(E):the probability that event E occurs.

【Distinguishable dice A and B】
(the number that dice A shows, the number dice B shows):event
If we only judge whether the numbers indicated by the dice are odd or even, the following four events will occur.
　　(odd, odd) (odd, even)

　　(even, odd) (even, even)
If each event occurs with equal probability, the probability is 1/4.
Therefore, P(①)=1/4, P(②)=1/2, P(③)=1/4 (1)
If we judge the number(1, 2, ···, 6) indicated by the dice, the following 36 events will occur.
(1, 1), (1, 3), (1, 5) (1, 2), (1, 4), (1, 6)
(3, 1), (3, 3), (3, 5) (3, 2), (3, 4), (3, 6)
(5, 1), (5, 3), (5, 5) (5, 2), (5, 4), (5, 6)

(2, 1), (2, 3), (2, 5) (2, 2), (2, 4), (2, 6)
(4, 1), (4, 3), (4, 5) (4, 2), (4, 4), (4, 6)
(6, 1), (6, 3), (6, 5) (6, 2), (6, 4), (6, 6)
If each event occurs with equal probability, the probability is 1/36.
Therfore
P(①)=9×(1/36)=1/4, P(②)=18×(1/36)=1/2, P(③)=9×(1/36)=1/4 (2)
(2) matches (1).

【Indistinguishable two dice】
(odd, even)is the same event as(even, odd).
Thererore, if we only judge whether the numbers indicated by the dice are odd or even, the following three events will occur.
　　(odd, odd)

　　(even, odd) (even, even)
If each event occurs with equal probability, the probability is 1/3.
Therefore
P(①)=1/3, P(②)=1/3, P(③)=1/3 (3)
(1, 3) is the same event as (3, 1).
If we judge the number(1, 2, ···, 6) indicated by the dice, the following 21 events will occur.
(1, 1)
(3, 1), (3, 3)
(5, 1), (5, 3), (5, 5)

(2, 1), (2, 3), (2, 5) (2, 2)
(4, 1), (4, 3), (4, 5) (4, 2), (4, 4)
(6, 1), (6, 3), (6, 5) (6, 2), (6, 4), (6, 6)
If each event occurs with equal probability, the probability is 1/21.
Therefore
P(①)=6×(1/21)=2/7, P(②)=9×(1/21)=3/7, P(③)=6×(1/21)=2/7 (4)
(4) contradicts (3).

[arjunsinha]

Sir it's time to explain Born-Oppenheimer approximation (Just a small request)

[timuralmabetov]

spot on, as always! thanks for sharing with us!

[adrinfpv]

You are an awesome teacher, love your videos. I am still waiting for the explanation, WHY does the square of a wave function represent the probability? I understand Einstein inspired Born, but the derivation is missing. Can you help enlighten us?

[Theories_stuff]

Sir, can we say that integration of mod psi square is a distribution of energy through out the x axis in a given region as generally amplitude square represents the energy.

[KipIngram]

Actually it contains information about what those quantities WILL BE - because they don't exist until you measure them. For example, position doesn't exist until the system is in a position eigenstate, which it will be as soon as you do a position measurement. As far as the position before you measure? Don't do that. Don't ask about it. It doesn't exist.

[ELECTRONICS_TIMES]

The best and clear explanation sir 👌
9:08 What if only modulus instead of modulus square? Without considering right hand terms complex and its conjugate.

16:23 How einstein got that idea (square the amplitudes of light gives probability of occurrence of photon)?

[riyanshraj]

I would love to see you teach general relativity

[HM-pbkd]

How much quantum mechanics do you need for IPhO?

The focus of the exam mainly lies on classical mechanics, but the quantum physics portion is not properly drfined for the exam.

[hg]

Good day, professor. Could you please let me know the book name you've shown in minute 16 of this video?

[ajittiwari]

Is there any paid lectures on Quantum Mechanics Where Divyajyoti Sir completes all the lectures on Quantum Mechanics 😮😍

[lowersaxon]

Your lectures are excellent, imho. The Schroedinger equation has to be called the Schroedinger equation, nevertheless. Greetings to sunny India.

[owaisfarooq]

How can we proof max born statistical interpretation mathematically