The function is reflected in the y axis. The function is symmetrical due to the modulus x so the -inf to 0 is the same as the 0 to inf so you can just do 2* 0t to inf
Basically the function has the interval: e^-k|x| = { e^kx for x < 0 { e^-kx for x > 0 This implies the function is symmetrical about the y-axis, so the area under the curve for the interval (-infinity to 0) is equal to the area under the curve for the interval (0 to +infinity) -- you can graph this using an arbitrary number for k if you want visual proof. Thus, you can just integrate over one interval and multiply it by 2 and get the same answer.
Why does the lower boundary and upper boundary changes from infinity ♾ to 0 and positive infinite? And why is it multiplied by 2 after the change occur?
When you multiply psi by its complex conjugate that part becomes e^-iwt*e^iwt = e^-iwt+iwt = e^0 = 1. It doesn't go anywhere, it just evaluates to 1 so you don't need to write it since multiplying by 1 doesn't change anything.
When you multiply by the conjugate, the sign of i switches and then it's just addition which cancels out the terms in the exponents. Look at properties of exponents to see how that works.
Do you think it is logical that if the future is unfolding relative to the atoms, if we look down at the individual atoms we will find probability? This is an invitation to see a theory on the nature of time! In this theory we have an emergent uncertain future continuously coming into existence relative to the spontaneous absorption and emission of photon energy. Within such a process the wave particle duality of light and matter in the form of electrons is forming a blank canvas that we can interact with forming the possible into the actual! The future is unfolding with each photon electron coupling or dipole moment relative to the atoms of the periodic table and the individual wavelengths of the electromagnetic spectrum. As part of a universal process of energy exchange that forms the ever changing world of our everyday life the ‘past’ has gone forever. At the smallest scale of this process the ‘past’ is represented by anti-matter annihilation with the symmetry between matter and anti-matter representing the symmetry between the future and the past as the future unfolds photon by photon. In such a theory the mathematics of quantum mechanics represents the physics of ‘time’ with the classical physics of Newton representing processes over a period of time, as in Newton’s differential equations. In my videos I explain how this process is relative to temperature and the phase changes of matter.
Bro...you can't mumble on something like this. Is that how you were taught? C'mon bro. Practice explaining this or teaching it to a couple of people before putting yourself out there, trying to explain something that you yourself are learning.
Dam. What an absolutely brilliant idea for asmr.
great video. Really helped me with my physics assignment :)
where does the 2 multiplying the A at 03:12 come from? please help
Its the property of integral
conjugate of i cancels each other ( conjugate of e^-iwt would be e^iwt .. so e^-iwt+iwt=e^0=1)
how does one get rid of the absolute x. always multiply by 2?
The function is reflected in the y axis. The function is symmetrical due to the modulus x so the -inf to 0 is the same as the 0 to inf so you can just do 2* 0t to inf
I can’t understand 2A
Basically the function has the interval:
e^-k|x| = { e^kx for x < 0
{ e^-kx for x > 0
This implies the function is symmetrical about the y-axis, so the area under the curve for the interval (-infinity to 0) is equal to the area under the curve for the interval (0 to +infinity) -- you can graph this using an arbitrary number for k if you want visual proof.
Thus, you can just integrate over one interval and multiply it by 2 and get the same answer.
If the function is odd.
Why does the lower boundary and upper boundary changes from infinity ♾ to 0 and positive infinite? And why is it multiplied by 2 after the change occur?
Check out even and odd functions, you'll get it.
Why didn't conjugate cancel e^(-λ|x|) at the start?
I believe only the imaginary part of the function is conjugated
why e^-i2wt disappears?
conjugate of i cancels each other ( conjugate of e^-iwt would be e^iwt .. so e^-iwt+iwt=e^0=1)
why does the e^i2wt drop out?
When you multiply psi by its complex conjugate that part becomes e^-iwt*e^iwt = e^-iwt+iwt = e^0 = 1. It doesn't go anywhere, it just evaluates to 1 so you don't need to write it since multiplying by 1 doesn't change anything.
@@uhuihiuhuihi
thanks, helps a lot!!
How to we get X eqaution? 6:00
expectation value equation *
This is an amazing video, which helped a lot! But the only problem is that you seem nervous and the sound's too low, but other than that, good job.
Do you need to learn about eigenvectors and eigenvalues for this problems
no
The people commenting don’t realize half the purpose of his videos, it’s right in his channel name. Look up ASMR.
How you remove -iwt
When you multiply by the conjugate, the sign of i switches and then it's just addition which cancels out the terms in the exponents. Look at properties of exponents to see how that works.
Right at the end shouldn't p-out equal e^-(2/√2)?
2/sqrt(2) is by definition the same as sqrt(2)
Muito bom! salvador da Pátria! Tava precisando dessa resolução! Obrigado! Thank's!
please increase the sound
Terms are not explain
its good but showing on the screen is less,its audio voice is too low
This would have been a perfect video if you didnt mumble. Still helped me none the less
Steps not explained and volume is very low
And video is also very slow
you seem to be doubtful at some steps
explain is fast and noise willbe enable to listen
Your sound is very low
It's ASMR,it's supposed to be low.
Plz speak loudly
speak up...
Do you think it is logical that if the future is unfolding relative to the atoms, if we look down at the individual atoms we will find probability? This is an invitation to see a theory on the nature of time! In this theory we have an emergent uncertain future continuously coming into existence relative to the spontaneous absorption and emission of photon energy. Within such a process the wave particle duality of light and matter in the form of electrons is forming a blank canvas that we can interact with forming the possible into the actual! The future is unfolding with each photon electron coupling or dipole moment relative to the atoms of the periodic table and the individual wavelengths of the electromagnetic spectrum. As part of a universal process of energy exchange that forms the ever changing world of our everyday life the ‘past’ has gone forever. At the smallest scale of this process the ‘past’ is represented by anti-matter annihilation with the symmetry between matter and anti-matter representing the symmetry between the future and the past as the future unfolds photon by photon. In such a theory the mathematics of quantum mechanics represents the physics of ‘time’ with the classical physics of Newton representing processes over a period of time, as in Newton’s differential equations. In my videos I explain how this process is relative to temperature and the phase changes of matter.
Quantum with the sex voice
Bro...you can't mumble on something like this. Is that how you were taught? C'mon bro. Practice explaining this or teaching it to a couple of people before putting yourself out there, trying to explain something that you yourself are learning.
Very shabby work ..!! Lacks adequate explanation. It would have been better if this video wasn't made, because it didn't help a bit.