Final answer:
To find the norm of the function f(x) = cos(πx/L), one would calculate the L2 norm, which involves integrating the square of the function over [-L, L]. The correct norm is √(L/2). Therefore, the correct answer is option 1.
Step-by-step explanation:
The student is asking how to find the length or norm (denoted as ‖‖f‖‖) of the function f(x) = cos(πx/L) on the interval [-L,L]. In mathematical terms, this corresponds to finding the L2 norm of the function, which is defined as the square root of the integral of the square of the function over the given interval. The computation requires evaluating an integral involving the squared cosine function, and typically results in expressions involving Planck's constant (h) when associated with quantum mechanics context.
To calculate the norm of the function, we would integrate the square of the cosine function from -L to L. However, the norm of a cosine function can also be generally found through specific normalization conditions used in quantum mechanics, particularly when dealing with wave functions. In this case, there are references to normalization constants and square of the wave function that lead to the conclusion that the correct norm would be √(L/2)