Dealing with complex operation in Quantum mechanics

In summary, complex operations in quantum mechanics refer to mathematical operations involving complex numbers that are crucial in describing the behavior of particles at the quantum level. They allow us to understand wave-like behavior, probabilistic nature, and make predictions about quantum systems. Some common examples include the Hamiltonian operator and Pauli matrices. Scientists use mathematical tools, computer simulations, and experiments to deal with complex operations and validate their theories. Without these operations, our understanding of the universe would be incomplete.
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M. next
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In proving that for the norm to be preserved, U must be unitary. I ran across this:

Re(λ<ø|ψ>)=Re(λ<Uø|Uψ>)

if λ=i, it says that then it follows that Im(<ø|ψ>)=Im(<Uø|Uψ>), how's this? I know that Re(iz)=-Im(z) in complex, but here the inner product <ø|ψ> is not z, or is it?

If you could point out how this took place, I would be thankful!
 
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  • #2
Yes, <ø|ψ> is a complex number, if that's what you're asking - It's not entirely clear to me.
 
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Yes, thanks. I noticed that after I posted this!
 

FAQ: Dealing with complex operation in Quantum mechanics

1. What is meant by "complex operation" in quantum mechanics?

In quantum mechanics, complex operations refer to mathematical operations that involve complex numbers. These operations are used to describe the behavior of particles at the quantum level, where classical mechanics cannot accurately predict their behavior.

2. How do complex operations affect the behavior of particles in quantum mechanics?

Complex operations play a crucial role in quantum mechanics as they allow us to describe the wave-like behavior of particles, such as superposition and entanglement. They also help us understand the probabilistic nature of quantum systems and make predictions about their behavior.

3. What are some common examples of complex operations used in quantum mechanics?

Some common examples of complex operations used in quantum mechanics include the Hamiltonian operator, which represents the total energy of a quantum system, and the Pauli matrices, which are used to describe the spin of particles.

4. How do scientists deal with complex operations in quantum mechanics?

To deal with complex operations in quantum mechanics, scientists use mathematical tools and techniques, such as linear algebra and complex analysis. They also use computer simulations and experiments to test and validate their theories and predictions.

5. Why are complex operations important in quantum mechanics?

Complex operations are essential in quantum mechanics because they allow us to accurately describe and understand the behavior of particles at the quantum level. Without these operations, we would not be able to make accurate predictions about the behavior of quantum systems, and our understanding of the universe would be incomplete.

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