In quantum mechanics, there is no strict upper limit to how small a wave can get. Waves can have arbitrarily short wavelengths, corresponding to high frequencies and high energy.
According to the wave-particle duality principle in quantum mechanics, particles such as electrons and photons can exhibit wave-like properties. The wavelength of a wave is inversely proportional to its momentum, so as the momentum increases, the wavelength decreases. Therefore, particles with high energy and momentum can be associated with very short wavelengths.
The concept of a "smallest possible" or "fundamental" wavelength is related to the Planck length, which is a theoretical length scale derived from fundamental constants of nature, such as the speed of light, Planck's constant, and the gravitational constant. The Planck length is approximately 1.6 x 10^-35 meters. It is often considered as the smallest meaningful length scale in the context of our current understanding of physics.
However, it's important to note that the Planck length does not represent the smallest possible wavelength or the smallest possible wave. It is simply a scale at which our current understanding of physics breaks down, and quantum gravitational effects become significant. At scales smaller than the Planck length, it is expected that a theory of quantum gravity would be needed to describe the underlying physics accurately.
In summary, in the framework of quantum mechanics, there is no strict upper limit to how small a wave can get. Waves can have arbitrarily short wavelengths corresponding to high energies. The Planck length represents a scale at which our current understanding of physics reaches its limits, but it does not define a fundamental limit to the size of a wave.