Schrodinger equation in terms of complex conjugate

In summary, the Schrodinger equation in terms of complex conjugate is a fundamental equation in quantum mechanics that describes the time evolution of a quantum system. It is written as iħ∂ψ/∂t = Ĥψ*, where i is the imaginary unit, ħ is the reduced Planck's constant, ψ is the wave function, Ĥ is the Hamiltonian operator, and * denotes the complex conjugate. The complex conjugate is used in the equation to account for the non-commutativity of operators and represents the Hermitian conjugate of an operator. It is necessary for accurately predicting the behavior of particles in a quantum system and ensuring the conservation of probability. Therefore, the Schrod
  • #1
QuantumDuality
10
0
I know there's a similar post, but i didn't understand it. Why the derivative respect to t in terms of the complex conjugate of ψ is:
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instead of being the original S.E in terms of ψ*
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or the equation in terms of ψ with the signs swapped
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  • #2
One is simply applying conjugation to the equation as a whole. This yields an equation which is valid provided the original is valid. Some c-number conjugation rules that may be helpful are,

  1. ##(a b)^\ast = a^\ast b^\ast##
  2. ##(a + b)^\ast = a^\ast + b^\ast##
  3. ##(i)^\ast = -i##
  4. ##(\frac{\partial \psi}{\partial t})^\ast = \frac{\partial \bar\psi}{\partial t}##
 
  • #3
I got it!. I always forget to use the product rule, Thanks
 

1. What is the Schrodinger equation in terms of complex conjugate?

The Schrodinger equation in terms of complex conjugate is a fundamental equation in quantum mechanics that describes the time evolution of a quantum system. It is written as:

iħ∂ψ/∂t = Ĥψ*

where i is the imaginary unit, ħ is the reduced Planck's constant, ψ is the wave function, Ĥ is the Hamiltonian operator, and * denotes the complex conjugate.

2. How is the complex conjugate used in the Schrodinger equation?

The complex conjugate is used in the Schrodinger equation to account for the non-commutativity of operators in quantum mechanics. It allows the equation to be written in terms of the Hamiltonian operator, which represents the total energy of a system.

3. What does the complex conjugate represent in the Schrodinger equation?

The complex conjugate represents the Hermitian conjugate of an operator in the Schrodinger equation. In quantum mechanics, Hermitian operators are used to represent physical observables, such as position, momentum, and energy.

4. Why is the complex conjugate necessary in the Schrodinger equation?

The complex conjugate is necessary in the Schrodinger equation because it ensures that the probability of finding a particle in a certain state remains constant over time. This is known as the conservation of probability and is a fundamental principle in quantum mechanics.

5. Can the Schrodinger equation be solved without using the complex conjugate?

No, the Schrodinger equation cannot be solved without using the complex conjugate. The complex conjugate is an essential part of the equation and is necessary for describing the time evolution of a quantum system accurately. Without it, the equation would not accurately predict the behavior of particles in a quantum system.

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