Parth G | Quantum Energy is NOT REAL. @ParthGChannel | Uploaded 1 year ago | Updated 7 hours ago
The formula for calculating the total energy of a system in quantum mechanics has the imaginary number, i, in it. Does this mean that energy is imaginary in quantum mechanics?
In classical physics, as well as in quantum mechanics, "energy" is a very useful mathematical concept that allows us to predict how a system will behave in different situations. This is primarily done through the use of the Law of Conservation of Energy. In classical physics it is important, therefore, that "energy" is a real, non-negative quantity. But then why does the total energy operator in quantum mechanics have the imaginary number in it?
In quantum mechanics, we often deal with a system's "wave function" - a complete mathematical description of the system, which allows us to calculate the probabilities of getting different experimental results if we were to make a measurement on the system. This wave function has both real and imaginary parts.
If we wanted to measure the energy of the system we are studying, the theoretical equivalent of that is "applying" (i.e. premultiplying) an operator to the wave function of the system. To measure a system's position, we apply the position operator. To measure its energy, we apply the total energy operator. The result of applying this operator, in a mathematical sense, is an eigenvalue (a REAL value) multiplied by the original wave function of the system (assuming the measurement does not change the system's state).
The real eigenvalue is the measured quantity. If we applied the total energy operator to our system, then the real eigenvalue is the total energy of the system. In other words then, the energy of our system is NOT imaginary - it is very much real. However, the total energy OPERATOR, the thing we apply to to the wave function in order to "make our measurement", is not real. This being imaginary is not a problem though, as it essentially "cancels" out the imaginary parts of the wave function in order to give us a real-valued energy as the result of the experiment.
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MERCH - https://parth-gs-merch-stand.creator-spring.com/
INSTAGRAM - @parthvlogs
PATREON - patreon.com/parthg
MUSIC CHANNEL - Parth G's Shenanigans
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Quantum Physics Book I Enjoy: https://amzn.to/3sxLlgL
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Timestamps:
0:00 - Energy in Classical and Quantum Physics
2:55 - Quantum Wave Functions and Energy Operators
The formula for calculating the total energy of a system in quantum mechanics has the imaginary number, i, in it. Does this mean that energy is imaginary in quantum mechanics?
In classical physics, as well as in quantum mechanics, "energy" is a very useful mathematical concept that allows us to predict how a system will behave in different situations. This is primarily done through the use of the Law of Conservation of Energy. In classical physics it is important, therefore, that "energy" is a real, non-negative quantity. But then why does the total energy operator in quantum mechanics have the imaginary number in it?
In quantum mechanics, we often deal with a system's "wave function" - a complete mathematical description of the system, which allows us to calculate the probabilities of getting different experimental results if we were to make a measurement on the system. This wave function has both real and imaginary parts.
If we wanted to measure the energy of the system we are studying, the theoretical equivalent of that is "applying" (i.e. premultiplying) an operator to the wave function of the system. To measure a system's position, we apply the position operator. To measure its energy, we apply the total energy operator. The result of applying this operator, in a mathematical sense, is an eigenvalue (a REAL value) multiplied by the original wave function of the system (assuming the measurement does not change the system's state).
The real eigenvalue is the measured quantity. If we applied the total energy operator to our system, then the real eigenvalue is the total energy of the system. In other words then, the energy of our system is NOT imaginary - it is very much real. However, the total energy OPERATOR, the thing we apply to to the wave function in order to "make our measurement", is not real. This being imaginary is not a problem though, as it essentially "cancels" out the imaginary parts of the wave function in order to give us a real-valued energy as the result of the experiment.
Thanks for watching, please do check out my links:
MERCH - https://parth-gs-merch-stand.creator-spring.com/
INSTAGRAM - @parthvlogs
PATREON - patreon.com/parthg
MUSIC CHANNEL - Parth G's Shenanigans
Here are some affiliate links for things I use!
Quantum Physics Book I Enjoy: https://amzn.to/3sxLlgL
My Camera: https://amzn.to/2SjZzWq
ND Filter: https://amzn.to/3qoGwHk
Timestamps:
0:00 - Energy in Classical and Quantum Physics
2:55 - Quantum Wave Functions and Energy Operators
