# Shifted solution to the time kernel equation

## Abstract

The solution to the time kernel equation with the boundary conditions *T*(*q*,*q*) = *q*/2 and *T*(*q*,*−q*) = 0 correspond to the quantum time of arrival 𝒯_{TOA} ∝ *T*(*q*,*q*'). Here, we investigate a different set of conditions, i.e., *T*(*q*,*q*) = *q*/2 and *T*(*q*,*−q*) = *−*2*iβ**q*, for some constant *β*. We show that these conditions correspond to the shifted solution 𝒯_{TOA} + *β*ℏ**H**^{−1}, where **H** is the Hamiltonian.

## Downloads

## Issue

## Article ID

SPP-2021-PC-13

## Section

Poster Session C (Theoretical and Mathematical Physics)

## Published

2021-10-01

## How to Cite

[1]

RAE Farrales and EA Galapon, Shifted solution to the time kernel equation,

*Proceedings of the Samahang Pisika ng Pilipinas***39**, SPP-2021-PC-13 (2021). URL: https://proceedings.spp-online.org/article/view/SPP-2021-PC-13.