Dickfore said:It is a general rule that the energy spectrum is discrete for finite motions, i.e. motions in which the particle cannot be found infinitely far away.
jtbell said:I think this needs to be refined a bit. How about the simple harmonic oscillator? Discrete energy eigenvalues, but the wave function only approaches zero as x goes to infinity, never quite reaching it.
Discrete eigenvalues refer to a set of distinct, individual values that can be assigned to a system or object. These values are typically represented by integers or whole numbers. On the other hand, continuous eigenvalues refer to a range of values that can be assigned to a system or object. These values are typically represented by real numbers.
Discrete eigenvalues are commonly used in the study of discrete systems, such as quantum systems, where the energy levels are quantized. Continuous eigenvalues are used in the study of continuous systems, such as classical mechanics, where the energy levels can take on any value within a range.
Yes, a system can have both discrete and continuous eigenvalues. This is often the case in quantum mechanics, where a particle's energy levels may have both discrete and continuous components.
Discrete and continuous eigenvalues are two distinct types of eigenvalues, but they are related in the sense that they both describe the possible values that a system or object can have. In some cases, a system may have a combination of both discrete and continuous eigenvalues.
The calculation of discrete and continuous eigenvalues depends on the specific system or object being studied. In general, discrete eigenvalues can be determined through the use of matrices and linear algebra, while continuous eigenvalues can be determined through the use of differential equations and calculus.