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pardesi
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what is the use of representing wavefunctions say [tex]\psi(x,t)=A\cos(kx-\omega t)[/tex] by [tex]\psi(x,t)=Ae^{i(kx-\omega t)}[/tex] when we actually mean the real part
pardesi said:yes i saw some but how cwn we be so sure that whatever we do using the complex numbers is right withoput checking them with the cos and sin
jostpuur said:If the PDE is linear, then that gives the correct result because the real trigonometric functions can be written as linear combinations of complex exponential functions.
Count Iblis said:You don't necessarily need to take the real part. You can just as well represent the wave by a complex number by identifying the amplitude with the absolute value of the complex number and the phase by the phase of the complex number.
Representing wavefunctions as an exponential allows us to simplify mathematical calculations and make them more manageable. It also provides a clearer understanding of the behavior and properties of wavefunctions.
By representing wavefunctions as an exponential, we can better visualize and analyze the behavior of particles in the quantum world. This representation helps us understand the probabilistic nature of quantum mechanics and how it differs from classical mechanics.
Yes, wavefunctions can be represented as any type of exponential function, including complex exponentials. The choice of the specific exponential function depends on the physical system being studied and the properties of the wavefunction that need to be represented.
The Schrödinger equation describes the behavior of quantum systems and is based on the representation of wavefunctions as an exponential. This mathematical relationship allows us to predict the evolution of a quantum system over time and make calculations about its properties.
While representing wavefunctions as an exponential is a useful tool, it is not always the most efficient or accurate method. In some cases, other mathematical representations may be more suitable for describing certain properties of a wavefunction or for solving specific problems in quantum mechanics.