Spiros Konstantogiannis

8 Questions 191 Answers 0 Followers

Questions related from Spiros Konstantogiannis

Does there exist a real sequence with the following properties?

Does there exist a real sequence, say (xn), with the following properties? (i) (xn) has non-zero terms and converges to zero (ii) The limit set of abs(xn+1\xn), i.e. the set containing the limits...

24 May 2021 7,625 3 View

Can the form of the momentum operator, in position space, be derived from qualitative physical arguments?

In standard quantum mechanics textbooks, the form of the momentum operator, in position space, is either given as definition, i.e. they write that the momentum operator is –id/dx (times the...

18 January 2019 8,992 5 View

In one-dimensional quantum mechanics, can the form of the potential be determined from the spectrum of the Hamiltonian?

In one-particle, one-dimensional quantum mechanics, if the spectrum of the Hamiltonian is given, can the form of the potential be determined? For instance, can all potentials with spectrum of the...

28 November 2018 9,343 18 View

Is it physically correct to impose mathematical conditions on the wave function pointwisely, i.e. at individual points of the physical space?

Due to the position-momentum uncertainty, it is impossible to measure the position of a microscopic particle exactly. This means that it is impossible to measure the probability density, i.e. the...

01 January 1970 1,122 3 View

Referring to abstract branches of mathematics, like topology, what is it that we generally call intuition and how it can be developed?

Referring to standard textbooks, one finds frequent appeals to readers’ intuition, when fundamental theorems are proved or basic definitions are explained. What exactly is intuition in such an...

01 January 1970 5,372 3 View

Is the Hermite basis the only orthonormal basis of the Schwartz space that can be calculated in closed form?

The Schwartz space of rapidly decreasing functions consists of all infinitely differentiable complex-valued functions on R that vanish at infinity, along with their derivatives, more rapidly than...

01 January 1970 3,494 4 View

Presentation of the Riemann integral via Cauchy sequences of Riemann sums

A sequential, if-and-only-if criterion of Riemann integrability that follows from the Riemann’s definition of the integral, states that a function on a closed and bounded interval is Riemann...

01 January 1970 1,142 13 View

On the definition of limit superior/inferior of a sequence of real numbers.

The limit superior/inferior of a sequence in R can be introduced in different ways. One way to define the previous limits is by considering the sequence of suprema/infima of the successive tails...

01 January 1970 9,936 18 View