Schrodinger Equation for a Bra Vector

In summary, the complex conjugate of a ket vector in the Schrodinger equation is derived by swapping the sign on the complex number when operating on the bra function, which gives the same result as operating on the ket without swapping the sign. The i in the denominator is also conjugated to eliminate the negative sign and may sometimes be moved to the numerator for simplification.
  • #1
nateHI
146
4
The Schrodinger equation for the complex conjugate of a ket vector is:

d/dt<sai(t)| = -(<sai(t)|H)/(i*hcross)

How do you derive the above equation from the normal form of the schrodinger equation? I'm mostly confused by where the negative sign is coming from.

Thanks
 
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  • #2
The bra function has the signs of all complex numbers swapped, so by swapping the sign on the complex number in your equation when it operates on the bra function it gives the same result as if you operated on the ket without swapping the sign.
 
  • #3
I get it now. I was making a silly mistake. You need to conjugate everything including the i in the denominator. Thanks.
 
  • #4
nateHI said:
I get it now. I was making a silly mistake. You need to conjugate everything including the i in the denominator. Thanks.

You sometimes also see the i moved to the numerator since -(i/i) is the same as -1 but cancels out the negative sign when 2 of the i's are multiplied.
 

Related to Schrodinger Equation for a Bra Vector

1. What is the Schrodinger Equation for a Bra Vector?

The Schrodinger Equation for a Bra Vector is a mathematical equation that describes the time evolution of a quantum mechanical system. It is a fundamental equation in quantum mechanics and is used to calculate the probability of finding a quantum system in a particular state.

2. Who first developed the Schrodinger Equation for a Bra Vector?

The Schrodinger Equation for a Bra Vector was developed by Austrian physicist Erwin Schrodinger in 1926. He derived the equation as a way to describe the behavior of quantum particles, such as electrons, in a system.

3. How does the Schrodinger Equation for a Bra Vector differ from the Schrodinger Equation for a Ket Vector?

The Schrodinger Equation for a Bra Vector and the Schrodinger Equation for a Ket Vector are essentially the same equation, but written in different mathematical notations. In bra-ket notation, the bra vector represents the initial state of a system, while the ket vector represents the final state.

4. What is the significance of the Schrodinger Equation for a Bra Vector in quantum mechanics?

The Schrodinger Equation for a Bra Vector is one of the key equations in quantum mechanics and is used to predict the behavior of quantum systems. It allows scientists to calculate the probability of a particle being in a certain state at a given time and has been instrumental in understanding the behavior of subatomic particles.

5. How is the Schrodinger Equation for a Bra Vector applied in real-world situations?

The Schrodinger Equation for a Bra Vector has a wide range of applications in fields such as quantum chemistry, material science, and electronics. It is used to model the behavior of atoms, molecules, and other quantum systems, and has led to many important discoveries and technological advancements.

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